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

1,1

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...

Links

Table of n, a(n) for n=1..33.

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 *)

Prog

(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

Crossrefs

Cf. A006509, A112877.

Sequence in context: A044252 A044633 A158123 * A044414 A044795 A092229

Adjacent sequences: A370948 A370949 A370950 * A370952 A370953 A370954

Keyword

nonn

Author

N. J. A. Sloane, Mar 07 2024

Extensions

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

Status

approved