What are the first several terms in the following sequential set.
... (29,11,5), (37,8,4), (46,8,3), (56,10,6) ...

(In reply to re: Solution by Corey)

For (x,y,z),

x is the "central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts" -- 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379, ...;

y is the "sum of exponents in prime-power factorization of C(4n,n-2)" -- 0, 3, 5, 5, 5, 9, 9, 11, 8, 8, 10, 12, 13, 15, 15, 16, 13, 16, 17, 16, 16, 18, 20, 22, 18, 20, 21, 20, 20, 22, 24, 25, 24, 25, 26, 26, 24, 28, 28, 29, 24, 28, 29, 29, 28, 29, 32, 34, 31, 31, 33, 31, 31, 34, 32, 34, 30, 33, 34, 37, 37, 40, 43, 42, 37, 39, 40, 41, 41, 41, 43, 44, 40, 45, 46, 46, 45, 47, ...;

and,
z is the "number of letters in the English name of n, excluding spaces and hyphens" -- 4 (zero) , 3 (one), 3 (two), 5 (three), 4 (four), 4 (five), 3 (six), 5 (seven), 5 (eight), 4 (nine), 3 (ten), 6 (eleven), 6 (twelve), 8 (thirteen), 8 (fourteen), 7 (fifteen), 7 (sixteen), 9 (seventeen), 8 (eighteen), 8 (nineteen), 6 (twenty), ...

The given terms-- (29,11,5), (37,8,4), (46,8,3), (56,10,6) -- are the eigth, ninth, tenth, and eleventh terms of the sequences.

Posted by Dej Mar on 2007-07-13 23:12:44