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

Author

Michael De Vlieger, Apr 29 2019

Keywords

• nonn

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).

Examples

			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).
		

Links

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

Crossrefs

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

Programs

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]]]

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