A112877 Zeros in Cald's sequence: positions k such that A006509(k) = 0.

117, 199, 381, 427, 521, 721, 1151, 1997, 3625, 6607, 12269, 23209, 41133, 75441, 141209, 266969, 507701, 968373, 1851971, 3549473, 6817481, 13115259, 25267949, 48750929, 94173137, 182122379, 352587759, 683348381, 1325663485, 2419811401, 4551835269, 8705190801, 16798251617, 32575310493

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Example

A006509(117) = 0 and A006509(k) > 0 for k < 117, so a(1) = 117.

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{b = a[n - 1], p = Prime[n - 1]}, If[ b - p > 0 && Position[t, b - p] == {}, b - p, If[ Position[t, b + p] == {}, b + p, 0]]]; t = {1}; Do[ AppendTo[t, a[n]], {n, 2, 270000}]; Flatten[ Position[t, 0]] (* Robert G. Wilson v, Oct 29 2005 *)

Prog

(Python)
from itertools import count, islice
from sympy import nextprime
def A112877_gen(): # generator of terms
    a, aset, p = 1, {1}, 2
    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
            yield c
        aset.add(a)
        p = nextprime(p)
A112877_list = list(islice(A112877_gen(), 10)) # Chai Wah Wu, Mar 04 2024

Crossrefs

Cf. A006509, A112878, A117128, A117129.

A370951 gives first differences.

Sequence in context: A272388 A272389 A201021 * A064180 A050245 A351574

Adjacent sequences: A112874 A112875 A112876 * A112878 A112879 A112880

Keyword

nonn

Author

Klaus Brockhaus, Oct 24 2005

Extensions

a(15) and a(16) from Robert G. Wilson v, Oct 29 2005

a(17) and a(18) from Klaus Brockhaus, Jan 01 2006

a(19)-a(26) from Donovan Johnson, Feb 18 2010

a(27)-a(29) from Chai Wah Wu, Mar 04 2024

a(30)-a(34) from Martin Ehrenstein, Mar 07 2024 (see A370951)

More than the usual number of terms are shown in order to include the new terms from A370951. - N. J. A. Sloane, Mar 10 2024

Status

approved