A057023 Largest odd factor of (n-th prime-1); k when n-th prime is written as k*2^m+1 [with k odd].

1, 1, 1, 3, 5, 3, 1, 9, 11, 7, 15, 9, 5, 21, 23, 13, 29, 15, 33, 35, 9, 39, 41, 11, 3, 25, 51, 53, 27, 7, 63, 65, 17, 69, 37, 75, 39, 81, 83, 43, 89, 45, 95, 3, 49, 99, 105, 111, 113, 57, 29, 119, 15, 125, 1, 131, 67, 135, 69, 35, 141, 73, 153, 155, 39, 79, 165, 21, 173, 87

Offset: 1

Author

Henry Bottomley, Jul 24 2000

Keywords

• nonn
• easy

Examples

			a(5)=5 because 5th prime is 11 and 11=5*2^1+1.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

Cf. A057024.

Programs

Mathematica

Table[p = Prime[n]; ie = IntegerExponent[p - 1, 2]; (p - 1)/2^ie, {n, 100}] (* Zak Seidov, Mar 25 2014 *)

PARI

lista(nn) = forprime (p=2, nn, my(m = p-1); print1(m >> valuation(m, 2), ", ")); \\ Michel Marcus, Jan 30 2016

PARI

a(n) = {my(m = prime(n) - 1); m >> valuation(m, 2);} \\ Michel Marcus, Jan 30 2016

Formula

a(n) = A000265(A000040(n)-1) = A000265(A006093(n)) =(A000040(n)-1)/A007814(A000040(n)-1) = A006093(n)/A023506(n).