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
Offset: 3
Keywords
Examples
a(4) = A001220(1)^2 = 1093^2 = 1194649. The only known square base-2 pseudoprimes are the squares of the Wieferich primes (A001220).
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.
Crossrefs
Programs
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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] -
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);}
Formula
a(n) = ((n-2)*k^2 - (n-4)*k)/2, where k = A371760(n).
Comments