A169643 Numbers k such that neither composite(k)+-1 is composite.

1, 2, 6, 10, 19, 28, 42, 51, 75, 79, 104, 114, 138, 148, 152, 178, 187, 212, 221, 247, 278, 338, 348, 372, 423, 465, 490, 504, 525, 539, 669, 679, 683, 709, 729, 848, 858, 873, 883, 909, 961, 1028, 1071, 1080, 1089, 1104, 1202, 1221, 1247, 1251, 1354, 1363

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A066246(A014574(n)). - Reinhard Zumkeller, Apr 06 2010

Example

a(1) = 1 because composite(1) - 1 = 3 = prime and composite(1) + 1 = 5 = prime.

Maple

Comp:= remove(isprime, [$4..2000]): nC:= nops(Comp):
select(t -> isprime(Comp[t]-1) and isprime(Comp[t]+1), [$1..nC]); # Robert Israel, Oct 21 2024

Mathematica

Position[Select[Range[2000], CompositeQ], _?(AllTrue[#+{1, -1}, PrimeQ]&), 1, Heads->False]// Flatten (* Harvey P. Dale, Jan 16 2024 *)

Prog

(PARI) listA169643(lim) = { my(v=List(), k=1); forcomposite(c=4, lim, if(isprime(c+1)&&isprime(c-1), listput(v, k)); k++); Vec(v) }; \\ Bruce Nye, Jun 07 2026
(Python)
from itertools import islice
from sympy import nextprime
def A169643_gen(): # generator of terms
    p, q, c = 2, 3, 1
    while True:
        if (r:=q-p-1)==1:
            yield c
        c += r
        p, q = q, nextprime(q)
A169643_list = list(islice(A169643_gen(), 30)) # Chai Wah Wu, Jun 07 2026

Crossrefs

Cf. A002808, A014574, A066246.

Sequence in context: A054273 A127567 A360420 * A005993 A028247 A209535

Adjacent sequences: A169640 A169641 A169642 * A169644 A169645 A169646

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 04 2010

Extensions

Corrected by Ray Chandler, Apr 05 2010

Status

approved