A371759 - OEIS

A371759

a(n) is the smallest n-gonal number that is a Fermat pseudoprime to base 2 (A001567), or -1 if no such number exists.

561, 1194649, 7957, 561, 23377, 341, 129889, 1105, 35333, 561, 204001, 31609, 2940337, 1105, 493697, 8481, 13981, 1905, 88561, 41665, 10680265, 1729, 107185, 264773, 449065, 6601, 2165801, 23001, 1141141, 13981, 272251, 4369, 17590957, 15841, 137149, 2821, 561

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OFFSET

3,1

COMMENTS

The corresponding indices of the n-gonal numbers are 33, 1093, 73, 17, 97, ... (A371760).

LINKS

Amiram Eldar, Table of n, a(n) for n = 3..10000

Eric Weisstein's World of Mathematics, Polygonal Number.

Eric Weisstein's World of Mathematics, Poulet Number.

Wikipedia, Polygonal number.

Wikipedia, Pseudoprime.

Index entries for sequences related to pseudoprimes.

FORMULA

a(n) = ((n-2)*k^2 - (n-4)*k)/2, where k = A371760(n).

EXAMPLE

a(4) = A001220(1)^2 = 1093^2 = 1194649. The only known square base-2 pseudoprimes are the squares of the Wieferich primes (A001220).

MATHEMATICA

p[k_, n_] := ((n-2)*k^2 - (n-4)*k)/2; pspQ[n_] := CompositeQ[n] && PowerMod[2, n - 1, n] == 1; a[n_] := Module[{k = 2}, While[! pspQ[p[k, n]], k++]; p[k, n]]; Array[a, 50, 3]

PROG

(PARI) p(k, n) = ((n-2)*k^2 - (n-4)*k)/2;

ispsp(n) = !isprime(n) && Mod(2, n)^(n-1) == 1;

a(n) = {my(k = 2); while(!ispsp(p(k, n)), k++); p(k, n); }

CROSSREFS

Cf. A001220, A001567, A293622, A293623, A322130, A321868, A321870, A322123, A322160, A371760.

Sequence in context: A097061 A290497 A258839 * A213867 A139089 A202562

Adjacent sequences: A371756 A371757 A371758 * A371760 A371761 A371762

KEYWORD

nonn

AUTHOR

Amiram Eldar, Apr 05 2024

STATUS

approved