1,3

Conjecture: Given the infinite set of sequences generated from the pairwise operation on A000594 (A097806^k * A000594), k = 24, (A128380) is the only sequence in the set with a zero. The sequence generated from k=23 = (1, -1, -47, 23, 1081, 47, -15939, ...). Analogous conjecture with the partial sum operator: (Cf. A128378, A128379); in which zeros are conjectured to occur only with k=23 and k=24. A128380 mod 24 = 1, 0, 0, 0, 0, 0, -4, 0, 0, 16, ...

Pairwise operation performed 24 times on A000594

Nest[Prepend[Most[#] + Rest[#], First[#]] &, RamanujanTau[Range[30]], 24] (* Amiram Eldar, Jan 08 2025 *)

Cf. A000594, A097806, A128378, A128379.

Sequence in context: A124354 A033979 A033368 * A298451 A094658 A136455

Adjacent sequences: A128377 A128378 A128379 * A128381 A128382 A128383

Gary W. Adamson, Feb 28 2007

More terms from Amiram Eldar, Jan 08 2025

approved