A156784 Primes : if sums of prime number and 8 consecutive prime numbers on-left-and-on-right are also primes.

29, 83, 127, 131, 157, 173, 197, 241, 389, 577, 619, 1129, 1201, 1259, 1361, 1367, 1429, 1439, 1601, 1663, 1723, 1783, 1787, 1811, 2017, 2083, 2153, 2237, 2287, 2351, 2371, 2591, 2659, 2699, 2819, 3163, 3209, 3373, 3407, 3433, 3467, 4013, 4051, 4217

Offset

1,1

Comments

3+5+7+11+13+17+19+23+29=127(prime);29+31+37+41+43+47+53+59+61=401(prime),... prime(n)+prime(n-1)+prime(n-2)+prime(n-3)+prime(n-4)+..+prime(n-8) are primes and prime(n)+prime(n+1)+prime(n+2)+prime(n+3)+prime(n+4)+..+prime(n+8) are also primes.

Links

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

Mathematica

lst={}; Do[p0=Prime[n+0]; p1=Prime[n+1]; p2=Prime[n+2]; p3=Prime[n+3]; p4=Prime[n+4]; p5=Prime[n+5]; p6=Prime[n+6]; p7=Prime[n+7]; p8=Prime[n+8]; p9=Prime[n+9]; p10=Prime[n+10]; p11=Prime[n+11]; p12=Prime[n+12]; p13=Prime[n+13]; p14=Prime[n+14]; p15=Prime[n+15]; p16=Prime[n+16]; If[PrimeQ[p0+p1+p2+p3+p4+p5+p6+p7+p8]&&PrimeQ[p8+p9+p10+p11+p12+p13+p14+p15+p16], AppendTo[lst, p8]], {n, 8!}]; lst
Transpose[Select[Partition[Prime[Range[600]], 17, 1], PrimeQ[Total[Take[#, 9]]] && PrimeQ[ Total[Take[#, -9]]]&]][[9]] (* Harvey P. Dale, Jan 29 2013 *)

Crossrefs

Cf. A156781, A156782, A156783

Sequence in context: A153680 A097722 A268612 * A142592 A343683 A255187

Adjacent sequences: A156781 A156782 A156783 * A156785 A156786 A156787

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 15 2009

Status

approved