A235622 Primes whose base-8 representation also is the base-7 representation of a prime.

2, 3, 5, 19, 53, 89, 109, 131, 257, 293, 307, 347, 349, 433, 523, 557, 683, 739, 811, 853, 881, 907, 937, 941, 1061, 1097, 1117, 1201, 1427, 1621, 1693, 1733, 1747, 1861, 1873, 1889, 1907, 2141, 2267, 2341, 2467, 2677, 2699, 2803, 2861, 2917, 2953, 3163, 3253, 3307, 3433

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

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

E.g., 19 = 23_8 and 23_7 = 17 are both prime.

Mathematica

pb87Q[n_]:=Module[{idn8=IntegerDigits[n, 8]}, Max[idn8]<7&&PrimeQ[ FromDigits[ idn8, 7]]]; Select[Prime[Range[500]], pb87Q] (* Harvey P. Dale, Dec 13 2016 *)

Prog

(PARI) is(p, b=7, c=8)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 8, 7)&&print1(vector(#d=digits(p, 7), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 7, 8)

Crossrefs

Cf. A235630, 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: A118625 A031133 A352604 * A235637 A028490 A004064

Adjacent sequences: A235619 A235620 A235621 * A235623 A235624 A235625

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved