A235471 Primes whose base-8 representation also is the base-3 representation of a prime.

2, 17, 73, 521, 577, 593, 1097, 1153, 4177, 8713, 33353, 33857, 37889, 41617, 65537, 65609, 69697, 70289, 70793, 74897, 262153, 262657, 266369, 331777, 331921, 336529, 336977, 529489, 533129, 533633, 590921, 594953, 598537, 2098241, 2101249, 2102417, 2134529

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.

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

Seems to be a subsequence of A066649 and A123364.

Since the trailing digit of the base 7 expansion must (like all others) be less than 3, this is a subsequence of A045381.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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

Example

E.g., 17 = 21_8 and 21_3 = 7 are both prime.

Mathematica

b8b3pQ[n_]:=Module[{id8=IntegerDigits[n, 8]}, Max[id8]<3&&PrimeQ[ FromDigits[ id8, 3]]]; Select[Prime[Range[160000]], b8b3pQ] (* Harvey P. Dale, Mar 16 2019 *)

Prog

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

Crossrefs

Cf. A231478, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A307851 A054568 A338087 * A297411 A183175 A060352

Adjacent sequences: A235468 A235469 A235470 * A235472 A235473 A235474

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved