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%I #13 Mar 31 2019 03:43:09
%S 1,9,91,205,362,519,634,1202,3075,11620,19197,32786,67401,67947,
%T 473326,587793,1215895,1361552,1998403,2532886,3039732,5138070,
%U 7058483,9465973,20128072,76214152
%N Where records occur in A239866.
%C The record values are 17, 40, 44, 58, 62, 68, 72, 106, 138, 144, 146, 190, 238, 240, 248, 258, 264, 290, 292, 340, 346, 348, 358, 378, 448, 452, ... - _Amiram Eldar_, Mar 31 2019
%e It starts with a(1) = 1, that is for p_1 = 2 we have 17 (in A239866)
%e Then a(2) = 9 because for p_9 = 23 we have 40 > 17.
%e Again a(3) = 91 because for p_91 = 467 we have 44 > 40. Etc.
%p P:=proc(q) local a, b, c, d, n, t; t:=0;
%p for n from 1 to q do a:=1; b:=ithprime(n); c:=b; d:=b-1;
%p while not isprime(d) do a:=a+1; c:=nextprime(c); d:=d+c; od;
%p if a>t then t:=a; print(n); fi; od; end: P(10^6);
%t a[n_] := Module[{s = -1, k = 0, p = Prime[n]}, While[!PrimeQ[s], s += p; p = NextPrime[p]; k++]; k]; am = 0; s={}; Do[a1 = a[n]; If[a1 > am, am = a1; AppendTo[s, n]], {n, 1, 70000}]; s (* _Amiram Eldar_, Mar 31 2019 *)
%Y Cf. A000040, A239864, A239865, A239866.
%K nonn,more
%O 1,2
%A _Paolo P. Lava_, Mar 28 2014
%E a(12)-a(26) from _Amiram Eldar_, Mar 31 2019
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