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A235126 Primes whose base-10 representation also represents a prime in base 17. 3
2, 3, 5, 7, 23, 29, 43, 61, 67, 83, 137, 139, 191, 197, 227, 241, 263, 313, 331, 461, 577, 593, 599, 607, 683, 739, 821, 863, 937, 953, 1013, 1033, 1039, 1051, 1297, 1303, 1327, 1459, 1619, 1693, 1721, 1787, 1811, 1877, 1949 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A090713 for a similar sequence whose definition works "in the opposite direction".

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The decimal representation of prime 23, considered as a number written in base 17, stands for 2*17+3 = 37, which is also prime, therefore 23 is in the sequence.

MAPLE

filter:= proc(p) local L;

  if not isprime(p) then return false fi;

  L:= convert(p, base, 10);

  isprime(add(L[i]*17^(i-1), i=1..nops(L)))

end proc:

select(filter, [2, seq(i, i=3..10000, 2)]); # Robert Israel, Apr 25 2017

MATHEMATICA

Select[Prime@ Range@ 300, PrimeQ@ FromDigits[IntegerDigits@ #, 17] &] (* Michael De Vlieger, Jan 03 2016 *)

PROG

(PARI) is(p, b=17)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows the production of similar sequences for other bases b > 9 (which can be given as an optional 2nd argument), but does not do the required check for bases b < 10.

CROSSREFS

Cf. A235110 and other sequences in the range A090707 - A091924.

Sequence in context: A069556 A210110 A235144 * A309248 A267014 A113611

Adjacent sequences:  A235123 A235124 A235125 * A235127 A235128 A235129

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 03 2014

STATUS

approved

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Last modified October 1 06:00 EDT 2020. Contains 337442 sequences. (Running on oeis4.)