

A110096


Least positive integer which, when added to each of 2^1, ..., 2^n, yields all primes. (If none exists, define the term to be 0.).


1



1, 1, 3, 3, 15, 15, 1605, 1605, 19425, 2397347205, 153535525935, 29503289812425, 29503289812425
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OFFSET

1,3


COMMENTS

Dickson's conjecture implies that a(n) > 0 for all n. [Charles R Greathouse IV, Oct 11 2011]


LINKS

Table of n, a(n) for n=1..13.


EXAMPLE

a(5)=15 is the least positive integer which, when added to 2^1, 2^2, 2^3, 2^4, 2^5, yields all primes: 17, 19, 23, 31, 47.


MATHEMATICA

p[n_] := Table[2^i, {i, 1, n}]; f[k_, n_] := MemberQ[PrimeQ[k + p[n]], False]; r = {}; For[n = 1, n <= 9, n++, k = 1; While[f[k, n], k = k + 1]; r = Append[r, k]]; r


CROSSREFS

Sequence in context: A055634 A133221 A232097 * A157526 A208229 A153512
Adjacent sequences: A110093 A110094 A110095 * A110097 A110098 A110099


KEYWORD

nonn


AUTHOR

Joseph L. Pe, Sep 05 2005


EXTENSIONS

2397347205 from T. D. Noe, Sep 06 2005
a(11) from Don Reble (djr(AT)nk.ca), Sep 17 2005


STATUS

approved



