A342038 - OEIS

%I #10 Feb 27 2021 04:21:43

%S 1,2,3,5,6,4,9,11,7,15,18,20,21,23,13,29,30,33,35,12,39,41,22,16,25,

%T 17,53,54,28,63,65,34,69,37,75,78,81,83,43,89,45,19,32,49,99,105,111,

%U 113,38,58,119,60,125,64,131,67,135,138,70,47,73,153,31,52,79

%N a(n) is the index of the first occurrence of prime(n) in A307437.

%C a(n) is the first k such that the smallest m such that C_(2k) is a subgroup of (Z/mZ)* is m = prime(n), where C_(2k) is the cyclic group of order 2k and (Z/mZ)* is the multiplicative group of integers modulo m.

%C a(n) is well-defined since A307437((p-1)/2) = p for odd primes p.

%H Jianing Song, <a href="/A342038/b342038.txt">Table of n, a(n) for n = 2..500</a>

%e For n = 7, prime(n) = 17. The first k such that: (i) C_(2k) is a subgroup of (Z/17Z)*; (ii) there is no m < 17 such that C_(2k) is a subgroup of (Z/mZ)* is k = 4, so a(7) = 4.

%e For n = 21, prime(n) = 73. The first k such that: (i) C_(2k) is a subgroup of (Z/73Z)*; (ii) there is no m < 73 such that C_(2k) is a subgroup of (Z/mZ)* is k = 12, so a(21) = 12.

%o (PARI) a(n) = if(n>=2, my(p=prime(n)); for(k=1, oo, if(A307437(k)==p, return(k)))) \\ see A307437 for its program

%Y Cf. A307437, A342039.

%K nonn

%O 2,2

%A _Jianing Song_, Feb 26 2021