

A236356


Numbers such that their digits indicate bases k, 2<=k<=9, in which representation of n, read in decimal, is prime; a(n)=0, if there is no such base.


12



0, 3456789, 2456789, 3, 246789, 5, 4689, 57, 68, 379, 48, 9, 45, 0, 68, 59, 47, 0, 468, 0, 59, 37, 245, 0, 68, 5, 6, 59, 47, 0, 78, 0, 568, 39, 8, 0, 469, 7, 689, 0, 5, 0, 4789, 0, 6, 3, 24, 9, 8, 7, 0, 7, 4, 0, 4689, 5, 8, 3, 78, 0, 49, 0, 5, 9, 8, 9, 368, 5
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OFFSET

1,2


COMMENTS

Composite numbers n for which a(n)=0 we call absolute composite numbers.
Almost evidently that almost all integers are absolute composite numbers. Moreover, since the number of primes<=x containing no at least one digit is o(pi(x)), then, for almost all positions of prime n, a(n)=0. It is interesting to obtain an upper estimate of number of nonzero positions in the sequence, more exactly, than o(x/log(x)).
Only O(sqrt x) numbers up to x have nonzero values in this sequence.  Charles R Greathouse IV, Jan 24 2014


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..5000


EXAMPLE

Let n=29. In base 2,3,...,9 the representations of 29 are 11101,1002,131,104,45,41,35,32. In this list only 131 (base4) and 41 (base7) are primes. Thus a(29)=47.
If we want to find the sequence of numbers which representations in base 4,7, read in decimal, are primes, then we consider n's, such that a(n) contains digits 4,7. They are 2,3,5,17,29,43,...


CROSSREFS

Cf. A052026.
Sequence in context: A258517 A258510 A254997 * A082247 A036473 A154871
Adjacent sequences: A236353 A236354 A236355 * A236357 A236358 A236359


KEYWORD

nonn,base


AUTHOR

Vladimir Shevelev, Jan 23 2014


STATUS

approved



