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Numbers k such that A000217(k+2)^A000217(k+1) mod A000217(k) is a triangular number.
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%I #14 Feb 06 2021 22:10:07

%S 1,2,3,4,6,7,9,13,14,18,21,26,27,44,52,54,62,70,81,84,91,125,143,154,

%T 162,164,182,215,230,243,259,284,287,403,422,434,455,476,484,486,489,

%U 494,511,559,574,583,670,719,729,741,854,910,923,962,989,1022,1034,1054,1079,1118,1159,1178,1295

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

%H Robert Israel, <a href="/A340877/b340877.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p tri:= n -> n*(n+1)/2:

%p istri:= x -> issqr(1+8*x):

%p select(t -> istri(tri(t+2) &^ tri(t+1) mod tri(t)), [$1..10000]);

%o (PARI) tri(n) = n*(n+1)/2; \\ A000217

%o isok(n) = ispolygonal(lift(Mod(tri(n+2), tri(n))^tri(n+1)), 3); \\ _Michel Marcus_, Jan 25 2021

%Y Cf. A000217.

%K nonn

%O 1,2

%A _J. M. Bergot_ and _Robert Israel_, Jan 24 2021