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 A335575 Numbers k such that A000217(k)^A000217(k+1) mod A000217(k+2) is a triangular number. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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]); 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

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Last modified September 19 16:34 EDT 2021. Contains 347564 sequences. (Running on oeis4.)