A235474 Primes whose base-4 representation is also the base-5 representation of a prime.

2, 3, 11, 29, 31, 41, 101, 109, 139, 149, 151, 181, 199, 229, 239, 251, 269, 271, 281, 389, 409, 491, 509, 541, 547, 661, 751, 887, 911, 947, 991, 1021, 1051, 1061, 1069, 1091, 1151, 1279, 1289, 1381, 1409, 1471, 1549, 1709, 1759, 1801, 1999

Offset

1,1

Comments

This sequence is part of a two-dimensional array of sequences, given in the LINK, based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.

For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Example

11 = 23_4 and 23_5 = 13 are both prime, so 11 is a term.

Mathematica

Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 4], 5]]&] (* Harvey P. Dale, Dec 31 2017 *)

Prog

(PARI) is(p, b=5, c=4)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

Crossrefs

Cf. A235266, A235473, A152079, A235475 - A235479, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A330979 A336402 A335364 * A075641 A176316 A181956

Adjacent sequences: A235471 A235472 A235473 * A235475 A235476 A235477

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved