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A235639 Primes whose base-9 representation is also the base-6 representation of a prime. 27
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 (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

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.

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

PROG

(PARI) is(p, b=6, c=9)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)

(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)

CROSSREFS

Cf. A231481, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971A020449, A089981, A090707 - A091924, A235615 - A235638. See the LINK for further cross-references.

Sequence in context: A019377 A215320 A215357 * A040107 A254670 A348900

Adjacent sequences:  A235636 A235637 A235638 * A235640 A235641 A235642

KEYWORD

nonn,base,look

AUTHOR

M. F. Hasler, Jan 13 2014

STATUS

approved

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Last modified January 23 21:06 EST 2022. Contains 350515 sequences. (Running on oeis4.)