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A260350
Define g(k) = min(n: n >= 0, 2^n + k prime). Then a(n) = min(odd k: g(k) = n).
4
1, 3, 7, 23, 31, 47, 199, 83, 61, 257, 139, 953, 991, 647, 1735, 383, 511, 1337, 1069, 713, 271, 1937, 3223, 5213, 751, 8477, 4339, 353, 1501, 287, 829, 1553, 2371, 1811, 11185, 3023, 7381, 7937, 6439, 1433, 13975, 2897, 4183
OFFSET
0,2
COMMENTS
Previous name: a(n) = min(k : A067760((k-1)/2)) = n.
a(n) is the first odd number k for which 2^m + k is the first prime value, as m ranges from 0 to n, or 0 if no such k exists. Thus it is the first k for which A067760((k-1)/2) = n, and therefore also the first k for which you need to test primality of exactly n values to show that it is not a dual Sierpiński number.
In the name, g(n) = A067760(n) except for n=1. - Michel Marcus, Apr 07 2018
LINKS
FORMULA
For n>=2, a(n) = (min(k : A067760((k-1)/2)) = n). - Michel Marcus, Apr 07 2018
EXAMPLE
2^i + 7 is composite for i < 2 (with values 8, 9) but prime for i = 2 (11); the smaller odd numbers 1, 3 and 5 each yield a prime for smaller i, so a(2) = 7.
PROG
(PARI) g(k) = {my(j=0); while (!isprime(2^j+k), j++); j; }
a(n) = {my(k = 1); while(g(k) != n, k+=2); k; } \\ Michel Marcus, Apr 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo van der Sanden, Jul 23 2015
EXTENSIONS
New name from Hugo van der Sanden and Michel Marcus, Apr 07 2018
STATUS
approved