A370951 First differences of A112877 (zero terms in Cald's sequence A006509).

82, 182, 46, 94, 200, 430, 846, 1628, 2982, 5662, 10940, 17924, 34308, 65768, 125760, 240732, 460672, 883598, 1697502, 3268008, 6297778, 12152690, 23482980, 45422208, 87949242, 170465380, 330760622, 642315104, 1094147916, 2132023868, 4153355532, 8093060816, 15777058876

Offset: 1

Author

N. J. A. Sloane, Mar 07 2024

Keywords

• nonn

Comments

The terms essentially double at each step. The ratios of successive terms are 2.219512195, 0.2527472527, 2.043478261, 2.127659574, 2.150000000, 1.967441860, 1.924349882, 1.831695332, 1.898725687, 1.932179442, 1.638391225, 1.914081678, 1.916987292, 1.912176134, 1.914217557, 1.913630095, 1.918063177, 1.921124765, 1.925186539, 1.927099934, 1.929679007, 1.932327740, 1.934260814, 1.936260826, 1.938224550, 1.940338983, 1.941933414, 1.703444165, 1.948570058, 1.948081161, 1.948559605, 1.949455124...

Crossrefs

Cf. A006509, A112877.

Programs

Mathematica

nn = 2^20; c[_] := False; a[1] = j = 1; c[1] = True;
Differences@ Monitor[Reap[
    Do[p = Prime[n - 1];
     If[And[# > 0, ! c[#]], k = #,
        If[c[#], k = 0; Sow[n], k = #] &[j + p]] &[j - p];
Set[{c[k], j}, {True, k}], {n, 2, nn}]][[-1, 1]], n] (* Michael De Vlieger, Mar 07 2024 *)

Python

from itertools import count, islice
from sympy import nextprime
def A370951_gen(): # generator of terms
    a, aset, p, q = 1, {1}, 2, 0
    for c in count(2):
        if (b:=a-p) > 0 and b not in aset:
            a = b
        elif (b:=a+p) not in aset:
            a = b
        else:
            a = 0
            if q:
                yield c-q
            q = c
        aset.add(a)
        p = nextprime(p)
A370951_list = list(islice(A370951_gen(),10)) # Chai Wah Wu, Mar 07 2024

Extensions

a(29)-a(33) from Martin Ehrenstein, Mar 07 2024