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
Keywords
Examples
A006509(117) = 0 and A006509(k) > 0 for k < 117, so a(1) = 117.
Programs
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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 *) -
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
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