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].

%I A057023 #22 Aug 15 2024 07:04:52
%S A057023 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,
%T A057023 53,27,7,63,65,17,69,37,75,39,81,83,43,89,45,95,3,49,99,105,111,113,
%U A057023 57,29,119,15,125,1,131,67,135,69,35,141,73,153,155,39,79,165,21,173,87
%N A057023 Largest odd factor of (n-th prime-1); k when n-th prime is written as k*2^m+1 [with k odd].
%H A057023 Zak Seidov, <a href="/A057023/b057023.txt">Table of n, a(n) for n = 1..10000</a>
%H A057023 <a href="/index/Pri#riesel">Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime</a>
%F A057023 a(n) = A000265(A000040(n)-1) = A000265(A006093(n)) =(A000040(n)-1)/A007814(A000040(n)-1) = A006093(n)/A023506(n).
%e A057023 a(5)=5 because 5th prime is 11 and 11=5*2^1+1.
%t A057023 Table[p = Prime[n]; ie = IntegerExponent[p - 1, 2]; (p - 1)/2^ie, {n, 100}] (* _Zak Seidov_, Mar 25 2014 *)
%o A057023 (PARI) lista(nn) = forprime (p=2, nn, my(m = p-1); print1(m >> valuation(m, 2), ", ")); \\ _Michel Marcus_, Jan 30 2016
%o A057023 (PARI) a(n) = {my(m = prime(n) - 1); m >> valuation(m, 2);} \\ _Michel Marcus_, Jan 30 2016
%Y A057023 Cf. A057024.
%K A057023 nonn,easy
%O A057023 1,4
%A A057023 _Henry Bottomley_, Jul 24 2000