

A235126


Primes whose base10 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
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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^(i1), 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^(#di))*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



