A340877 Numbers k such that A000217(k+2)^A000217(k+1) mod A000217(k) is a triangular number.

1, 2, 3, 4, 6, 7, 9, 13, 14, 18, 21, 26, 27, 44, 52, 54, 62, 70, 81, 84, 91, 125, 143, 154, 162, 164, 182, 215, 230, 243, 259, 284, 287, 403, 422, 434, 455, 476, 484, 486, 489, 494, 511, 559, 574, 583, 670, 719, 729, 741, 854, 910, 923, 962, 989, 1022, 1034, 1054, 1079, 1118, 1159, 1178, 1295

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(5) = 6 is a term because A000217(6..8) are 21, 28, 36, 36^28 (mod 21) == 15, and 15 = A000217(5) is a triangular number.

Maple

tri:= n -> n*(n+1)/2:
istri:= x -> issqr(1+8*x):
select(t -> istri(tri(t+2) &^ tri(t+1) mod tri(t)), [$1..10000]);

Prog

(PARI) tri(n) = n*(n+1)/2; \\ A000217
isok(n) = ispolygonal(lift(Mod(tri(n+2), tri(n))^tri(n+1)), 3); \\ Michel Marcus, Jan 25 2021

Crossrefs

Cf. A000217.

Sequence in context: A050050 A222801 A117307 * A161890 A089388 A055494

Adjacent sequences: A340874 A340875 A340876 * A340878 A340879 A340880

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 24 2021

Status

approved