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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


%S 29,83,127,131,157,173,197,241,389,577,619,1129,1201,1259,1361,1367,

%T 1429,1439,1601,1663,1723,1783,1787,1811,2017,2083,2153,2237,2287,

%U 2351,2371,2591,2659,2699,2819,3163,3209,3373,3407,3433,3467,4013,4051,4217

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

%C 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.

%H Harvey P. Dale, <a href="/A156784/b156784.txt">Table of n, a(n) for n = 1..1000</a>

%t 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

%t Transpose[Select[Partition[Prime[Range[600]],17,1],PrimeQ[Total[Take[#,9]]] && PrimeQ[ Total[Take[#,-9]]]&]][[9]] (* _Harvey P. Dale_, Jan 29 2013 *)

%Y Cf. A156781, A156782, A156783

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 15 2009

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Last modified February 6 18:26 EST 2016. Contains 268049 sequences.