cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A117781 Total number of palindromic primes in base 6 below 6^n.

Original entry on oeis.org

3, 4, 10, 10, 31, 31, 126, 126, 571, 571, 2752, 2752, 14248, 14248, 73971, 73971, 389920, 389920, 2108414, 2108414, 11512078, 11512078
Offset: 1

Views

Author

Martin Renner, Apr 15 2006

Keywords

Comments

Every palindrome with an even number of digits is divisible by 11 (in base 6) and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits.

Links

Crossrefs

Partial sums of A117782.
Cf. A029974, A117701.
Cf. A117772, A117775, A117777, A117779, A117783, A117785, A117787.

Extensions

a(11)-a(22) from the data at A117782 added by Amiram Eldar, Mar 21 2021

A117782 Total number of palindromic primes in base 6 with n digits.

Original entry on oeis.org

3, 1, 6, 0, 21, 0, 95, 0, 445, 0, 2181, 0, 11496, 0, 59723, 0, 315949, 0, 1718494, 0, 9403664, 0
Offset: 1

Views

Author

Martin Renner, Apr 15 2006

Keywords

Comments

Every palindrome with an even number of digits is divisible by 11 (in base 6) and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits.
A palindromic prime > 3 in base 6 must start (and end) with either the digit 1 or the digit 5. - Chai Wah Wu, Dec 03 2015

Examples

			a(2) = 1, because 11(6) = 7(10), is the only palindromic prime with 2 digits. - _Michel Marcus_, Oct 11 2014

Links

Crossrefs

Cf. A029974, A117701.

Programs

  • Mathematica
    Length@ Select[Prime@ Range[PrimePi[6^# + 1], PrimePi[6^(# + 1)]], # == Reverse@ # &@ IntegerDigits[#, 6] &] & /@ Range[0, 8] (* Michael De Vlieger, Dec 06 2015 *)
  • PARI
    a(nd, b=6) = {if ((nd > 2) && ((nd % 2) == 0), return (0)); nb = 0; forprime(p = b^(nd-1), b^nd-1, d = digits(p, b); if (Pol(d) == Polrev(d), nb++);); nb;} \\ Michel Marcus, Oct 11 2014

Extensions

a(11)-a(12) from Michel Marcus, Oct 11 2014
a(13)-a(22) from Chai Wah Wu, Dec 03 2015
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