A333673 a(n) is the number of prime 5-digit palindromes in base n.

2, 3, 10, 18, 21, 41, 47, 64, 93, 106, 170, 171, 185, 227, 314, 345, 422, 464, 526, 571, 719, 806, 928, 972, 1179, 1237, 1354, 1508, 1754, 1778, 2116, 2108, 2401, 2529, 2862, 3010, 3188, 3362, 3580, 3820, 4218, 4330, 4817, 5033, 5488, 5516, 6225, 6343, 6759, 6870, 7497, 7704, 8151, 8660, 9267

Offset

2,1

Comments

a(n) is the number of primes of the form a*(n^4+1)+b*(n^3+n)+c*n^2 where 1<=a<n, 0<=b<n and 0<=c<n.

Links

Robert Israel, Table of n, a(n) for n = 2..250

Example

The a(4)=10 5-digit palindromes in base 4 are
257 = 10001_4
373 = 11311_4
409 = 12121_4
461 = 13031_4
509 = 13331_4
787 = 30103_4
839 = 31013_4
887 = 31313_4
907 = 32023_4
991 = 33133_4

Maple

f:= proc(n) nops(select(isprime, [seq(seq(seq(i*(n^4+1)+j*(n^3+n)+k*n^2, k=0..n-1), j=0..n-1), i=1..n-1)])) end proc:
map(f, [$2..60]);

Crossrefs

Cf. A117752.

Sequence in context: A350913 A066915 A339924 * A070253 A147673 A298345

Adjacent sequences: A333670 A333671 A333672 * A333674 A333675 A333676

Keyword

nonn,base

Author

Robert Israel, May 04 2020

Status

approved