A307805 a(n) = first position of prime(n) in A023503.

2, 4, 5, 10, 9, 16, 27, 43, 15, 17, 64, 35, 23, 40, 61, 28, 127, 73, 57, 104, 62, 66, 39, 41, 77, 111, 114, 117, 182, 49, 97, 56, 143, 102, 196, 155, 248, 119, 346, 69, 72, 181, 76, 137, 497, 139, 318, 388, 721, 401, 91, 92, 229, 96, 243, 249, 325, 258, 186, 103

Offset

1,1

Comments

A023503(n) = A006530(A006093(n)).

Apparent permutation of A071349(n) apart from A071349(1) = 1.

Let i = a(n). Sorting prime(n) in order of increasing i yields A112037 = {2, 3, 5, 11, 7, 23, 13, 29, 41, ...}. The product of the first j terms of A112037 = A071350(j).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

a(1) = 2 since prime(1) = gpf(prime(2) - 1), i.e., 2 = gpf(2).
a(2) = 4 since prime(2) = gpf(prime(4) - 1), i.e., 3 = gpf(6).
a(3) = 5 since prime(3) = gpf(prime(5) - 1), i.e., 5 = gpf(10).
a(4) = 10 since prime(4) = gpf(prime(10) - 1), i.e., 7 = gpf(28).

Mathematica

With[{s = Array[FactorInteger[Prime@ # - 1][[-1, 1]] &, 1000]}, Reap[Do[If[FreeQ[s, #], Break[], Sow@ FirstPosition[s, #][[1]]] &@ Prime@ i, {i, Length@ s}]][[-1, -1]]]

Prog

(PARI) { a = vector(60); pr = primes(#a); u = 1; n = 1;
forprime (p=3, oo, n++; f=factor(p-1); g=setsearch(pr, f[#f~, 1]);
if (g && !a[g], a[g]=n; while (a[u], print1 (a[u]", "); u++; if (u>#a, break (2))))) } \\ Rémy Sigrist, May 28 2019

Crossrefs

Cf. A006093, A006530, A023503, A071349, A112037.

Sequence in context: A173660 A353384 A335315 * A189767 A173817 A198383

Adjacent sequences: A307802 A307803 A307804 * A307806 A307807 A307808

Keyword

nonn

Author

Michael De Vlieger, Apr 29 2019

Status

approved