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The 1979 Series (Posted on 2013-08-27) Difficulty: 2 of 5
In the sequence 19796..., each digit after 6 is the sum, mod 10, of the preceding four digits. Show that ...1979... turns up again in the sequence, but that ...1980... never occurs at all.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution computer solution Comment 1 of 1

OPEN "1979sers.txt" FOR OUTPUT AS #2
a = 1: b = 9: c = 7: d = 9
ct = 4
PRINT #2, "1979";
FOR i = 1 TO 1560 * 3
  e = (a + b + c + d) MOD 10
  PRINT LTRIM$(STR$(e));
  PRINT #2, LTRIM$(STR$(e));
  ct = ct + 1: IF ct MOD 65 = 0 THEN PRINT #2,
   IF ct MOD 1560 = 0 THEN PRINT #2,
  a = b: b = c: c = d: d = e
NEXT
CLOSE

The references to 1560 and 65 in the above were made after the fact, upon seeing that the cycle length was 1560.

Three cycles are shown below, all beginning with 1979. The sequence 1980 can't be found, nor can 1 be found at the right edge, nor 19 nor 198, so it is not broken by the line breaks.


19796139923375833938337145773291572593967575417794777565393057574
39394519943513217334771941599479994137561917851152973101573617716
15354795565179297758777903913699716377307771277734153323195835176
93530193361333095712553581717615916175923937213396195161311619730
99198759903137459532993349957013150959363133073336571929113497332
53334333321957237910775989175259172997725153435570793989951499356
37178397769915499794991325119673516579781515231172111585979051512
97972537729539631992113723577217772391583731453356719303519831138
35952175585317671154111709739877138911901113611192359969375495318
79590379983999075136559543131835738315769791639978375383933837190
77374157709391257596779927751039350757989399019998513767339271996
59992999963751691730115747315657316771165359295510179747753277958
91314971187735277172773965337819538517143535693316333545717053536
71716591167597893776339169511631116973549193259958137909537493394
95756315545931813352333107197411394733703339833376957787915275934
17570917749777015398557529393495194935187173897714915949799491370
11912351107973651578117761153097950151747977037774539181997613778
57776777789153873190335121935851938113385957675530317121159611754
73932713341195611316119785991437594531329595879938999525131059598
13138573381571479118997387533893338719527379657754391707591279972
75158935525793439956999301371233972199109997499918751141735615792
31510731127111035974551567979275372795341319471132735727177273910
33736953301719853514331183359071750353121711091112597343771839114
51118111147359419370995363795453794339945751815590931363357833152

19796139923375833938337145773291572593967575417794777565393057574
39394519943513217334771941599479994137561917851152973101573617716
15354795565179297758777903913699716377307771277734153323195835176
93530193361333095712553581717615916175923937213396195161311619730
99198759903137459532993349957013150959363133073336571929113497332
53334333321957237910775989175259172997725153435570793989951499356
37178397769915499794991325119673516579781515231172111585979051512
97972537729539631992113723577217772391583731453356719303519831138
35952175585317671154111709739877138911901113611192359969375495318
79590379983999075136559543131835738315769791639978375383933837190
77374157709391257596779927751039350757989399019998513767339271996
59992999963751691730115747315657316771165359295510179747753277958
91314971187735277172773965337819538517143535693316333545717053536
71716591167597893776339169511631116973549193259958137909537493394
95756315545931813352333107197411394733703339833376957787915275934
17570917749777015398557529393495194935187173897714915949799491370
11912351107973651578117761153097950151747977037774539181997613778
57776777789153873190335121935851938113385957675530317121159611754
73932713341195611316119785991437594531329595879938999525131059598
13138573381571479118997387533893338719527379657754391707591279972
75158935525793439956999301371233972199109997499918751141735615792
31510731127111035974551567979275372795341319471132735727177273910
33736953301719853514331183359071750353121711091112597343771839114
51118111147359419370995363795453794339945751815590931363357833152

19796139923375833938337145773291572593967575417794777565393057574
39394519943513217334771941599479994137561917851152973101573617716
15354795565179297758777903913699716377307771277734153323195835176
93530193361333095712553581717615916175923937213396195161311619730
99198759903137459532993349957013150959363133073336571929113497332
53334333321957237910775989175259172997725153435570793989951499356
37178397769915499794991325119673516579781515231172111585979051512
97972537729539631992113723577217772391583731453356719303519831138
35952175585317671154111709739877138911901113611192359969375495318
79590379983999075136559543131835738315769791639978375383933837190
77374157709391257596779927751039350757989399019998513767339271996
59992999963751691730115747315657316771165359295510179747753277958
91314971187735277172773965337819538517143535693316333545717053536
71716591167597893776339169511631116973549193259958137909537493394
95756315545931813352333107197411394733703339833376957787915275934
17570917749777015398557529393495194935187173897714915949799491370
11912351107973651578117761153097950151747977037774539181997613778
57776777789153873190335121935851938113385957675530317121159611754
73932713341195611316119785991437594531329595879938999525131059598
13138573381571479118997387533893338719527379657754391707591279972
75158935525793439956999301371233972199109997499918751141735615792
31510731127111035974551567979275372795341319471132735727177273910
33736953301719853514331183359071750353121711091112597343771839114
51118111147359419370995363795453794339945751815590931363357833152

1979


  Posted by Charlie on 2013-08-27 18:07:02
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