A335575 Numbers k such that A000217(k)^A000217(k+1) mod A000217(k+2) is a triangular number.

1, 3, 5, 7, 8, 9, 10, 11, 13, 19, 20, 21, 23, 25, 29, 30, 31, 33, 34, 35, 36, 37, 43, 44, 45, 49, 50, 55, 56, 58, 59, 61, 62, 63, 66, 68, 70, 71, 72, 74, 75, 77, 79, 80, 81, 83, 85, 91, 93, 94, 103, 104, 106, 108, 115, 117, 118, 119, 124, 125, 127, 128, 131, 138, 139, 143, 144, 153, 154, 155, 157

Offset

1,2

Comments

It appears that in most of these cases, A000217(k)^A000217(k+1) mod A000217(k+2) is either 1 or A000217(k).

Links

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

Example

a(3) = 5 is a member because A000217(5..7) are 15, 21, 28, and 15^21 == 15 (mod 28) where 15 is a triangular number.

Maple

tri:= n -> n*(n+1)/2:
istri:= n -> issqr(1+8*n):
select( n -> istri(tri(n) &^ tri(n+1) mod tri(n+2)), [$1..1000]);

Mathematica

Position[Partition[Accumulate[Range[200]], 3, 1], _?(OddQ[Sqrt[1+8*PowerMod[ #[[1]], #[[2]], #[[3]]]]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Nov 26 2022 *)

Prog

(PARI) tri(n) = n*(n+1)/2; \\ A000217
isok(n) = ispolygonal(lift(Mod(tri(n), tri(n+2))^tri(n+1)), 3); \\ Michel Marcus, Jan 26 2021

Crossrefs

Cf. A000217, A340877.

Sequence in context: A020491 A168501 A173186 * A047746 A111638 A324334

Adjacent sequences: A335572 A335573 A335574 * A335576 A335577 A335578

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 26 2021

Status

approved