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a(n) is the smallest number k such that A361929(k) = prime(n), or -1 if no such prime exists.
1

%I #14 Apr 09 2023 05:27:01

%S 1,2,7,10,26,177,508,13812,73873,4638434,4638435,1874400183,

%T 114936835817

%N a(n) is the smallest number k such that A361929(k) = prime(n), or -1 if no such prime exists.

%C It is conjectured that all primes appear in A361929.

%t K = {2}; R = {1}; r = 2; z = 1; While[Length@R < 9, z++; p = 2; While[MemberQ[K[[Length@K - GCD[z - 1, Last@K] + 1 ;; Length@K]], p], p = NextPrime[p]]; AppendTo[K, p]; If[p > r, AppendTo[R, z]; r = p]; If[Length@K > NextPrime[r], K = K[[Length@K - NextPrime[r] ;; Length@K]]]]; Print[R]

%Y Cf. A361929.

%K nonn,more

%O 1,2

%A _Samuel Harkness_, Mar 30 2023

%E a(12)-a(13) from _Kevin Ryde_, Apr 01 2023