A366093 Indices of records in A366092.

0, 11, 22, 27, 58, 61, 110, 126, 161, 545, 566, 592, 747, 775, 2286, 5343, 5360, 5741, 18245, 78272, 93999, 140690, 146338, 227734, 251721, 274297, 372294, 447238, 586777, 808500, 7185887, 10479806, 37485090, 85742340, 91332097, 111764212, 117522098, 556747657, 589122990

Offset: 1

Author

Paolo Xausa, Sep 29 2023

Keywords

• nonn
• hard

Crossrefs

Cf. A366092.

Programs

Mathematica

pDist[n_]:=If[PrimeQ[n],0,Min[NextPrime[n]-n,n-NextPrime[n,-1]]];
A366093list[upto_]:=Module[{r=-1,a={},d=Map[pDist,Prepend[Accumulate[Prime[Range[upto]]],0]]},Do[If[d[[i]]>r,r=d[[i]];AppendTo[a,i-1]],{i,upto}];a];
A366093list[10000]

Python

from itertools import count, islice
from sympy import prevprime, nextprime
def A366093_gen(): # generator of terms
    c, s, p = 2, 0, 1
    yield 0
    for i in count(1):
        if (m:=min((s:=s+(p:=nextprime(p)))-prevprime(s+1),nextprime(s)-s))>c:
            yield i
            c = m
A366093_list = list(islice(A366093_gen(),20)) # Chai Wah Wu, Oct 03 2023

Extensions

a(31)-a(39) from Michael S. Branicky, Oct 03 2023