(In reply to
thought on (c) by Charlie)
Allowing 1's in only the sum of the original integer adds only 3 new solutions:
N sqrt(N) sod(N) pod(sqrt(N))
81 9 9 9
1296 36 18 18
8649 93 27 27
110889 333 27 27
27269284 5222 40 40
But allowing 1's in the pod of the square root adds a lot:
8649 93 27 27
3663396 1914 36 36
4562496 2136 36 36
5363856 2316 36 36
26347689 5133 45 45
27269284 5222 40 40
28227969 5313 45 45
84879369 9213 54 54
228553924 15118 40 40
299739969 17313 63 63
455096889 21333 54 54
543495969 23313 54 54
26605850769 163113 54 54
36524943225 191115 45 45
36907788996 192114 72 72
45502009344 213312 36 36
398428588944 631212 72 72
658389433744 811412 64 64
662778348544 814112 64 64
707469396544 841112 64 64
3280854783969 1811313 72 72
3287378750769 1813113 72 72
3690709738884 1921122 72 72
Such allowing is in fact the secret to 1's expansion: it prevents the greater power of multiplication to outstrip the power of addition, as multiplication causes an exponential increase, vs addition's arithmetic increase. Even 2^10 exceeds 9*10.
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Posted by Charlie
on 2023-02-09 09:55:06 |
re: thought on (c)
