A239865 Where records occur in A239864.

1, 2, 44, 51, 111, 300, 357, 3603, 3779, 5326, 5372, 30817, 117498, 151450, 166877, 545114, 5941303, 14726486, 16436691, 17402909, 32947955, 77092704, 202485484, 328878332, 383238249, 435910049

Offset

1,2

Comments

The record values are 1, 16, 22, 40, 54, 64, 90, 94, 112, 180, 184, 192, 202, 204, 256, 368, 388, 390, 418, 460, 472, 500, ... - Amiram Eldar, Mar 31 2019

Links

Table of n, a(n) for n=1..26.

Example

It starts with a(1) = 1, that is for p_1 = 2 we have 1 in A239864.
Then a(2) = 2 because for p_2 = 3 we have 16 > 1.
Again a(3) = 44 because for p_44 = 193 we have 22 > 16. Etc.

Maple

P:=proc(q) local a, b, c, d, n, t; t:=0;
for n from 1 to q do a:=1; b:=ithprime(n); c:=b; d:=b+1;
while not isprime(d) do a:=a+1; c:=nextprime(c); d:=d+c; od;
if a>t then t:=a; print(n); fi; od; end: P(10^6);

Mathematica

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, 120000}]; s (* Amiram Eldar, Mar 31 2019 *)

Crossrefs

Cf. A000040, A239864, A239866, A239867.

Sequence in context: A392550 A156478 A156508 * A007367 A006313 A059737

Adjacent sequences: A239862 A239863 A239864 * A239866 A239867 A239868

Keyword

nonn,more

Author

Paolo P. Lava, Mar 28 2014

Extensions

a(13)-a(22) from Amiram Eldar, Mar 31 2019

a(23)-a(26) from Michael S. Branicky, Feb 10 2026

Status

approved