A065022 Composite n such that the sums of the composite numbers up to n, +/- 1, are twin primes.

4, 8, 290, 340, 352, 412, 489, 610, 774, 785, 1227, 1295, 1306, 1795, 1853, 1918, 1945, 2014, 2266, 2502, 2885, 3063, 3133, 3178, 3265, 3482, 3486, 3680, 3760, 3843, 3973, 3995, 4124, 4794, 5677, 5769, 5965, 6123, 7555, 7653, 7696, 7765, 7786, 8023

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

4+6+8 = 18 and 18 +/-1 are twin primes.

Mathematica

Composite[n_Integer] := (k = n + PrimePi[n] + 1; While[k - PrimePi[k] - 1 != n, k++ ]; k); s = 0; Do[m = Composite[n]; s = s + m; If[ PrimeQ[s - 1] && PrimeQ[s + 1], Print[m]], {n, 1, 10^4} ]

Prog

(PARI) is(n)=my(s); if(isprime(n), return(0)); forcomposite(k=4, n, s+=k); isprime(s-1)&&isprime(s+1) \\ Charles R Greathouse IV, Jan 02 2014
(PARI) s=0; forcomposite(n=4, 8023, s+=n; if(isprime(s-1) && isprime(s+1), print1(n", "))) \\ Charles R Greathouse IV, Jan 02 2014

Crossrefs

Cf. A014574, A053767.

Sequence in context: A085631 A074073 A090653 * A012994 A136386 A260726

Adjacent sequences: A065019 A065020 A065021 * A065023 A065024 A065025

Keyword

nonn

Author

Robert G. Wilson v, Nov 01 2001

Extensions

New name from Charles R Greathouse IV, Jan 02 2014

Status

approved