A235625 -id:A235625 - cp's OEIS frontend

A235626 Primes whose base-6 representation also is the base-5 representation of a prime.

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

Offset: 1

M. F. Hasler, Jan 13 2014

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.

			Both 13 = 21_6 and 21_5 = 11 are prime.

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

Cf. A235625, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

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

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 *)

is(p,b=5,c=6)=vecmax(d=digits(p,c))

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)

cp's OEIS Frontend

A235626 Primes whose base-6 representation also is the base-5 representation of a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI