A117129 Primes not occurring as |differences| in Cald's sequence A006509.

641, 1213, 2617, 2957, 3727, 5443, 9283, 17359, 33829, 66173, 131303, 264763, 494743, 957547, 1888157, 3753647, 7490797, 14961157, 29899357, 59773871, 119551489, 239106347, 478234723, 956607929, 1913366111, 3826828409, 7653840367, 15308666783, 30619196381, 57415599151

Offset: 1

Author

N. J. A. Sloane, Apr 20 2006

Keywords

• nonn

Comments

In other words, primes that do not occur as absolute values of differences of successive terms in Cald's sequence A006509.

Crossrefs

Cf. A006509, A112877.

Programs

Python

from itertools import count, islice
from sympy import nextprime
def A117129_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 p
        aset.add(a)
        p = nextprime(p)
A117129_list =  list(islice(A117129_gen(),10)) # Chai Wah Wu, Mar 04 2024

Formula

a(n) = prime(A112877(n) - 1).

Extensions

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

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

a(30) from Chai Wah Wu, Mar 10 2024