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

Author

Robert G. Wilson v, Nov 01 2001

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A014574, A053767.

Programs

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} ]

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

Extensions

New name from Charles R Greathouse IV, Jan 02 2014