A057024 -id:A057024 - cp's OEIS frontend

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

Henry Bottomley, Jul 24 2000

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

Cf. A057024.

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

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

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

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

A057026 Smallest prime of form (2n+1)*2^m-1 for some m, or 0 if no such prime exists.

Original entry on oeis.org

3, 2, 19, 13, 17, 43, 103, 29, 67, 37, 41, 367, 199, 53, 463, 61, 131, 139, 73, 311, 163, 5503, 89, 751, 97, 101, 211, 109, 113, 241663, 487, 251, 1039, 2143, 137, 283, 9343, 149, 307, 157, 647, 331, 2719, 173, 1423, 181, 743, 379, 193, 197, 103423, 823, 419

Offset: 0

Henry Bottomley, Jul 24 2000

nonn

If a(329) > 0 it is greater than 659*2^10000. - Robert Israel, Jul 01 2014
Indeed, a(329) > 659*2^100000 if it is nonzero. There does not appear to be a covering set, though, so probably a(329) > 0. - Charles R Greathouse IV, Jul 02 2014
a(329) = 659*2^800516 - 1 (found by David W Linton in 2004). - Robert Israel, Jul 04 2014

			a(5)=43 because 2*5+1=11 and smallest prime of the form 11*2^m-1 is 43 (since 10 and 21 are not prime)

Cf. A057024, A057025, A038699.

A057026:= proc(n)
local t;
     t:= 2*n;
     while not isprime(t) do t:= 2*t+1 od;
     t
end proc;
seq(A057026(n),n=0..328); # Robert Israel, Jul 01 2014

cp's OEIS Frontend

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

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