|
| |
|
|
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: A185275 A055634 A133221 * A157526 A208229 A153512
Adjacent sequences: A110093 A110094 A110095 * A110097 A110098 A110099
|
|
|
KEYWORD
|
nonn,changed
|
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), 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
|
| |
|
|
