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A235626 Primes whose base 6 representation also is the base 5 representation of a prime. 2
2, 3, 13, 43, 97, 223, 307, 337, 379, 433, 457, 547, 709, 727, 769, 811, 919, 1009, 1303, 1597, 1609, 1777, 1861, 1987, 2017, 2029, 2221, 2239, 2269, 2311, 2647, 2689, 2749, 2917, 3037, 3067, 3121, 3169, 3373, 3529, 3541, 3571, 3613, 3967, 4219, 4261, 4327, 4339 (list; graph; refs; listen; history; text; internal format)
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 Israel, 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., 13 = 21[6] and 21[5] = 11 both are prime.

MAPLE

P:= {seq(ithprime(i), i=1..10000)}:

f:= proc(p) local i, L;

  L:= convert(p, base, 5);

  add(L[i]*6^(i-1), i=1..nops(L))

end proc:

sort(convert(map(f, P) intersect P, list)); # Robert Israel, Jun 18 2019

MATHEMATICA

b65pQ[n_]:=Module[{idn6=IntegerDigits[n, 6]}, Max[idn6]<5&&PrimeQ[ FromDigits[ idn6, 5]]]; Select[Prime[Range[600]], b65pQ] (* Harvey P. Dale, Oct 13 2020 *)

PROG

(PARI) is(p, b=5, c=6)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)

(PARI) forprime(p=1, 3e3, is(p, 6, 5)&&print1(vector(#d=digits(p, 5), i, 6^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 6)

CROSSREFS

Cf. A235625, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A106866 A278139 A280005 * A164133 A226938 A301395

Adjacent sequences:  A235623 A235624 A235625 * A235627 A235628 A235629

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 13 2014

STATUS

approved

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)