A187766 Even numbers k such that prime(k) -+ k are both composite.

12, 20, 36, 38, 40, 46, 52, 56, 58, 60, 62, 64, 74, 78, 80, 86, 88, 112, 118, 120, 122, 124, 128, 132, 134, 136, 138, 140, 142, 146, 156, 160, 162, 164, 166, 170, 176, 182, 184, 186, 188, 190, 194, 198, 208, 210, 212, 216

Offset

1,1

Comments

Even numbers not in A064269 and not in A064402.

Interestingly, prime(12) = 37 and both 37 - 12 = 25 and 37 + 12 = 49 are squares. Is there another such n?

There is no other such n up through the first 15,000 terms of the sequence. - Harvey P. Dale, Mar 26 2026

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

Select[2*Range[200], !PrimeQ[Prime[#]+#]&&!PrimeQ[Prime[#]-#]&] (* Harvey P. Dale, Dec 24 2013 *)
Select[Range[2, 250, 2], AllTrue[Prime[#]+{#, -#}, CompositeQ]&] (* Harvey P. Dale, Mar 26 2026 *)

Prog

(PARI) {forstep(i=2, 220, 2, p=prime(i); if(!isprime(p-i)&&!isprime(p+i), print1(i", ")))}

Crossrefs

Cf. A064269, A064402.

Sequence in context: A026041 A299028 A082296 * A260905 A211415 A209973

Adjacent sequences: A187763 A187764 A187765 * A187767 A187768 A187769

Keyword

nonn

Author

Zak Seidov, Jan 04 2013

Status

approved