A235637 - OEIS

A235637

Primes whose base-7 representation also is the base-6 representation of a prime.

2, 3, 5, 19, 61, 89, 127, 131, 173, 211, 229, 257, 281, 383, 397, 421, 463, 467, 523, 547, 593, 617, 719, 757, 761, 859, 883, 911, 953, 967, 971, 1069, 1097, 1153, 1163, 1181, 1303, 1307, 1429, 1433, 1471, 1489, 1531, 1583, 1597, 1723, 1741, 1867, 1877, 1951, 1979, 1993, 2437

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OFFSET

1,1

COMMENTS

This sequence is part of the two-dimensional array of sequences 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.

LINKS

Robert Price, Table of n, a(n) for n = 1..14278

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

EXAMPLE

E.g., 19 = 25_7 and 25_6 = 17 are both prime.

PROG

(PARI) is(p, b=6, c=7)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)

(PARI) forprime(p=1, 3e3, is(p, 7, 6)&&print1(vector(#d=digits(p, 6), i, 7^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 6, 7)

CROSSREFS

Cf. A235636, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A031133 A352604 A235622 * A028490 A004064 A164061

Adjacent sequences: A235634 A235635 A235636 * A235638 A235639 A235640

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 13 2014

STATUS

approved