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A361502 Index of n-th prime in A359804.

%I A361502 #25 Jul 09 2025 05:00:17
%S A361502 2,3,4,8,13,42,347,3466,49012,528231,717126,63056215,1375559400,
%T A361502 7038527851
%N A361502 Index of n-th prime in A359804.
%C A361502 Theorem: Every prime appears in A359804. For proof see A359804.
%C A361502 It appears that the primes in A359804 appear in order.
%H A361502 Rémy Sigrist, <a href="/A361502/a361502.txt">C++ program</a>
%t A361502 nn = 2^20; c[_] = False; q[_] = 1;
%t A361502  i = 1; j = 2; c[1] = c[2] = True; u = 3;
%t A361502  {2}~Join~Reap[Monitor[Do[
%t A361502       (k = q[#]; While[c[k #], k++]; k *= #;
%t A361502          While[c[# q[#]], q[#]++]) &[(p = 2;
%t A361502         While[Divisible[i j, p], p = NextPrime[p]]; p)];
%t A361502       If[PrimeQ[k], Sow[n]; Print[n]];
%t A361502       Set[{c[k], i, j}, {True, j, k}];
%t A361502 If[k == u, While[c[u], u++]], {n, 3, nn}], n]][[-1, -1]] (* _Michael De Vlieger_, Mar 19 2023 *)
%o A361502 (C++) // See Links section.
%Y A361502 Cf. A359804, A361504.
%K A361502 nonn,more
%O A361502 1,1
%A A361502 _N. J. A. Sloane_, Mar 18 2023, based on a comment made by _Michael De Vlieger_ in A359804 in which he gave the values of a(1) to a(12)
%E A361502 a(13)-a(14) from _Rémy Sigrist_, Mar 19 2023