A085245 Least k such that k*2^n + 1 is a semiprime.

4, 2, 1, 2, 1, 1, 1, 6, 3, 2, 1, 1, 1, 6, 3, 2, 1, 2, 1, 1, 3, 2, 1, 3, 8, 4, 2, 1, 3, 2, 1, 1, 3, 7, 5, 5, 8, 4, 2, 1, 4, 2, 1, 3, 3, 7, 6, 3, 15, 9, 29, 28, 14, 7, 6, 3, 3, 8, 4, 2, 1, 4, 2, 1, 14, 7, 12, 6, 3, 3, 9, 5, 12, 6, 3, 8, 4, 2, 1, 3, 29, 18, 9, 18, 9, 10, 5, 13, 8, 4, 2, 1, 15, 12, 6, 3, 9, 6

Offset

1,1

Comments

The first few values of n such that 78557*2^n + 1 is a semiprime, where k = 78557 (the conjectured smallest Sierpinski number), are: 2, 3, 7, 15, 17, 18, 24, 60, 71, 89, 92, 107, 140, 143, 163,... Conjecture: there are infinitely many semiprimes of this form.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..500

Example

a(51)=29 because k*2^51 + 1 is not a semiprime for k=1,2,...28, but 29*2^51 + 1 = 63839 * 1022920073887 is.

Prog

(PARI) a(n) = my(k=1); while (bigomega(k*2^n + 1) != 2, k++); k; \\ Michel Marcus, Jul 02 2020

Crossrefs

Cf. A001358, A035050, A076336.

Sequence in context: A010313 A159823 A075826 * A327694 A348136 A235795

Adjacent sequences: A085242 A085243 A085244 * A085246 A085247 A085248

Keyword

nonn

Author

Jason Earls, Aug 11 2003

Status

approved