A355238 First occurrence of difference n between two consecutive terms of A000404. a(n) gives the upper term. The lower term is A355237.

18, 10, 5, 17, 25, 80, 97, 145, 386, 3060, 997, 1681, 4194, 6544, 1508, 8450, 9721, 22178, 10728, 5185, 16130, 154730, 58441, 31681, 52418, 401506, 176837, 101377, 105601, 678386, 241913, 501748, 393850, 284036, 685576, 1437389, 1751333, 3225616, 3439297, 2479634

Offset: 1

Author

Hugo Pfoertner, Jun 30 2022

Keywords

• nonn

Crossrefs

Cf. A000404, A355237.

Programs

Python

from itertools import count
from sympy import factorint
def A355238(n):
    m = 2
    for k in count(2):
        c = False
        for p in (f:=factorint(k)):
            if (q:= p & 3)==3 and f[p]&1:
                break
            elif q == 1:
                c = True
        else:
            if c or f.get(2,0)&1:
                if k-m == n:
                    return k
                m = k # Chai Wah Wu, Jul 01 2022

Formula

a(n) = A355237(n) + n.