A342038 a(n) is the index of the first occurrence of prime(n) in A307437.

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, 17, 53, 54, 28, 63, 65, 34, 69, 37, 75, 78, 81, 83, 43, 89, 45, 19, 32, 49, 99, 105, 111, 113, 38, 58, 119, 60, 125, 64, 131, 67, 135, 138, 70, 47, 73, 153, 31, 52, 79

Offset

2,2

Comments

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.

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

Links

Jianing Song, Table of n, a(n) for n = 2..500

Example

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.
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.

Prog

(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

Crossrefs

Cf. A307437, A342039.

Sequence in context: A194900 A194051 A195610 * A082654 A072636 A191741

Adjacent sequences: A342035 A342036 A342037 * A342039 A342040 A342041

Keyword

nonn

Author

Jianing Song, Feb 26 2021

Status

approved