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A307805 a(n) = first position of prime(n) in A023503. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A125728 A276608 A173660 * A189767 A173817 A198383

Adjacent sequences:  A307802 A307803 A307804 * A307806 A307807 A307808

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Apr 29 2019

STATUS

approved

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)