

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 A269956
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, Sep 17 2005


STATUS

approved



