

A235463


Primes whose base 6 representation also is the base 2 representation of a prime.


2



7, 37, 43, 223, 1297, 1303, 1549, 7993, 9109, 46663, 54469, 55987, 326593, 1679659, 1681129, 1727569, 1734049, 1967587, 2006461, 2007763, 2014027, 2015287, 10077919, 10125649, 10125691, 10133467, 10412107, 10413397, 11757349, 11766421, 11766427, 11766637
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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.
For further motivation and crossreferences, see sequence A235265 which is the main entry for this whole family of sequences.
When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=6, thus a subsequence of A077720.


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., 7 = 11[6] and 11[2] = 3 both are prime. 37 = 101[6] and 101[2] = 5 both are prime.


MATHEMATICA

b62Q[n_]:=Module[{idn6=IntegerDigits[n, 6]}, Max[idn6]<2&&AllTrue[ {FromDigits[ idn6, 6], FromDigits[idn6, 2]}, PrimeQ]]; Select[Prime[ Range[ 4, 780000]], b62Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 29 2020 *)


PROG

(PARI) is(p, b=2, c=6)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#di))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 6, 2)&&print1(vector(#d=digits(p, 2), i, 6^(#di))*d~, ", ")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(., 2, 6)


CROSSREFS

Cf. A065720 ⊂ A036952, A065721  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924, A235461  A235482. See the LINK for further crossreferences.
Sequence in context: A106924 A076285 A077720 * A127313 A217561 A003521
Adjacent sequences: A235460 A235461 A235462 * A235464 A235465 A235466


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 11 2014


STATUS

approved



