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%I #9 Apr 30 2021 11:42:20
%S 1,2,4,7,25,12,16,37,24,32,33,40,67,63,48,58,78,60,81,50,102,91,114,
%T 109,110,116,117,124,130,137,120,128,152,168,190,183,184,186,215,199,
%U 206,202,259,235,208,264,261,256,269,274,281,318,272,301,316,330,329,342,327,352,326,376,346,312
%N a(n) is the least k such that A343796(k) = n, or 0 if there is no such k.
%C a(n) is the least k such that there are exactly n distinct primes of the form A007504(k) mod p for the first k primes p.
%H Robert Israel, <a href="/A343798/b343798.txt">Table of n, a(n) for n = 0..1000</a>
%e a(4) = 25 because A007504(25) = 1060 and there are 4 primes of the form 1060 mod p for the first 25 primes p: 2 = 1060 mod 23, 3 = 1060 mod 7, 7 = 1060 mod 13 and 23 = 1060 mod 61, and 25 is the first k that produces exactly 4 primes in this way.
%p N:= 100: # for a(0)..a(N)
%p V:= Array(0..N): count:= 0:
%p P:= {}: p:= 1: t:= 0:
%p for n from 1 while count < 100 do
%p p:= nextprime(p); P:= P union {p}; t:= t+p;
%p v:= nops(select(isprime, map(s -> t mod s, P)));
%p if v <= N and V[v] = 0 then
%p V[v]:= n; count:= count+1;
%p fi
%p od:
%p convert(V,list);
%Y Cf. A007504, A343796.
%K nonn
%O 0,2
%A _J. M. Bergot_ and _Robert Israel_, Apr 29 2021
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