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A156784 Primes : if sums of prime number and 8 consecutive prime numbers on-left-and-on-right are also primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A255187 A273362

Adjacent sequences:  A156781 A156782 A156783 * A156785 A156786 A156787

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Feb 15 2009

STATUS

approved

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Last modified March 5 11:57 EST 2021. Contains 341823 sequences. (Running on oeis4.)