A117775 Total number of palindromic primes in base 3 below 3^n.

1, 1, 3, 3, 6, 6, 18, 18, 26, 26, 73, 73, 179, 179, 459, 459, 1179, 1179, 3004, 3004, 8111, 8111, 22183, 22183, 60789, 60789, 168641, 168641, 469689, 469689, 1322664, 1322664, 3691761, 3691761, 10390938, 10390938, 29502559, 29502559, 84012658, 84012658, 239417332, 239417332

Offset

1,3

Comments

Every palindrome with an even number of digits is divisible by 11 (in base 3) and therefore is composite (not prime). Hence there is no palindromic prime with an even number of digits.

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Palindromic Prime.

Formula

a(2*k-1) = a(2*k) for k >= 1. - Bernard Schott, Mar 23 2021

Example

a(5) = a(6) = 6 as the six palindromic primes below 3^5 are 2_10 = 2_3, 13_10 = 111_3, 23_10 = 212_3, 151_10 = 12121_3, 173_10 = 20102_3, 233_10 = 22122_3. There are no palindromic primes with 6 digits so a(5) = a(6). - David A. Corneth, Mar 21 2021

Crossrefs

Partial sums of A117776.

Cf. A029971, A117698.

Cf. A117772, A117777, A117779, A117781, A117783, A117785, A117787.

Sequence in context: A200905 A280510 A292128 * A243307 A021301 A016652

Adjacent sequences: A117772 A117773 A117774 * A117776 A117777 A117778

Keyword

nonn,base

Author

Martin Renner, Apr 15 2006

Extensions

a(15)-a(42) from the data at A117776 added by Amiram Eldar, Mar 21 2021

Status

approved