A247233 Smallest m such that A075323(m) = n-th odd prime, or zero, if no such m exists.

1, 2, 3, 4, 5, 11, 6, 7, 12, 8, 9, 29, 15, 10, 13, 16, 17, 14, 30, 23, 18, 19, 509, 24, 25, 20, 55, 21, 37, 26, 22, 35, 27, 31, 38, 33, 56, 28, 36, 43, 32, 34, 39, 41, 51, 45, 44, 53, 47, 40, 42, 65, 52, 46, 49, 67, 161, 48, 54, 63, 59, 66, 61, 50, 79, 57

Offset: 1

Author

Reinhard Zumkeller, Nov 29 2014

Keywords

• nonn

Comments

Conjecture: a(388) = 0, i.e., A065091(388) = 2683 doesn't occur in A075323;

for n with a(n) > 0: A075323(a(n)) = A065091(n) = A000040(n+1).

Examples

			Also a(389) = 0 (presumably), whereas subsequent terms (n > 389) are > 0:
393,443,421,350,397,455,368,433,387,352,356,382,384,366,372,392,374, ...
with corresponding odd primes:
2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777, ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..387

Crossrefs

Cf. A075323, A065091, A000040.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a247233 = (+ 1) . fromJust . (`elemIndex` a075323_list) . a065091

Mathematica

maxm = 3000;
A075321p[n_] := A075321p[n] = Module[{prevlist, i, p, q}, If[n == 1, Return[{3, 5}], prevlist = Array[A075321p, n-1] // Flatten]; For[i = 2, True, i++, p = Prime[i]; If[FreeQ[prevlist, p], q = p + 2*n; If[ PrimeQ[q] && FreeQ[prevlist, q], Return[{p, q}]]]]];
A075323[n_] := If[OddQ[n], A075321p[(n + 1)/2][[1]], A075321p[n/2][[2]]];
a[n_] := For[m = 1, m <= maxm, m++, If[A075323[m] == Prime[n + 1], Return[m]]] /. Null -> 0;
Array[a, 387] (* Jean-François Alcover, Feb 12 2018, after R. J. Mathar's program for A075321p *)