A235639 Primes whose base-9 representation is also the base-6 representation of a prime.

2, 3, 5, 19, 23, 41, 113, 127, 131, 163, 199, 271, 419, 433, 739, 743, 761, 919, 991, 1009, 1013, 1063, 1153, 1171, 1459, 1481, 1499, 1553, 1567, 1571, 1733, 1747, 1783, 1873, 1913, 2237, 2377, 2381, 2539, 2557, 2593, 2633, 2939, 3011, 3079, 3083, 3187, 3259, 3331, 3659

Offset: 1

Author

M. F. Hasler, Jan 13 2014

Keywords

• nonn
• base
• look

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.

Examples

			19 = 21_9 and 21_6 = 13 are both prime, so 19 is a term.
509 = 625_9 and 625_6 = 17 are both prime, but 625 is not a valid base-6 integer, so 509 is not a term.
		

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

Crossrefs

Cf. A231481, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235638. See the LINK for further cross-references.

Programs

Maple

R:= 2: x:= 2: count:= 1:
while count < 100 do
  x:= nextprime(x);
  L:= convert(x,base,6);
  y:= add(9^(i-1)*L[i],i=1..nops(L));
  if isprime(y) then count:= count+1; R:= R, y fi
od:
R; # Robert Israel, May 18 2020

PARI

is(p,b=6,c=9)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,3e3,is(p,9,6)&&print1(vector(#d=digits(p,6),i,9^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,6,9)