cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

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

Original entry on oeis.org

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

Views

Author

Jianing Song, Feb 26 2021

Keywords

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.

Examples

			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.
		

Crossrefs

Programs

  • 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
Showing 1-1 of 1 results.