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

%I A247233 #24 Feb 12 2018 11:37:00
%S A247233 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,
%T A247233 20,55,21,37,26,22,35,27,31,38,33,56,28,36,43,32,34,39,41,51,45,44,53,
%U A247233 47,40,42,65,52,46,49,67,161,48,54,63,59,66,61,50,79,57
%N A247233 Smallest m such that A075323(m) = n-th odd prime, or zero, if no such m exists.
%C A247233 Conjecture: a(388) = 0, i.e., A065091(388) = 2683 doesn't occur in A075323;
%C A247233 for n with a(n) > 0: A075323(a(n)) = A065091(n) = A000040(n+1).
%H A247233 Reinhard Zumkeller, <a href="/A247233/b247233.txt">Table of n, a(n) for n = 1..387</a>
%e A247233 Also a(389) = 0 (presumably), whereas subsequent terms (n > 389) are > 0:
%e A247233 393,443,421,350,397,455,368,433,387,352,356,382,384,366,372,392,374, ...
%e A247233 with corresponding odd primes:
%e A247233 2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777, ...
%t A247233 maxm = 3000;
%t A247233 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}]]]]];
%t A247233 A075323[n_] := If[OddQ[n], A075321p[(n + 1)/2][[1]], A075321p[n/2][[2]]];
%t A247233 a[n_] := For[m = 1, m <= maxm, m++, If[A075323[m] == Prime[n + 1], Return[m]]] /. Null -> 0;
%t A247233 Array[a, 387] (* _Jean-François Alcover_, Feb 12 2018, after _R. J. Mathar_'s program for A075321p *)
%o A247233 (Haskell)
%o A247233 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A247233 a247233 = (+ 1) . fromJust . (`elemIndex` a075323_list) . a065091
%Y A247233 Cf. A075323, A065091, A000040.
%K A247233 nonn
%O A247233 1,2
%A A247233 _Reinhard Zumkeller_, Nov 29 2014