A156971 Primes : if sums of prime number and 10 consecutive prime numbers on-left-and-on-right are also primes.

41, 103, 151, 157, 167, 173, 191, 331, 349, 353, 359, 421, 479, 487, 619, 677, 853, 883, 967, 1297, 1427, 1429, 1483, 1627, 2017, 2081, 2141, 2273, 2333, 2389, 2549, 2591, 2609, 2621, 2683, 2689, 2777, 3119, 3169, 4139, 4231, 4253, 4297, 4447, 4519, 4621

Offset

1,1

Comments

5+7+11+13+17+19+23+29+31+37+41=233(prime);41+43+47+53+59+61+67+71+73+79+83=677(prime),...

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]; p17=Prime[n+17]; p18=Prime[n+18]; p19=Prime[n+19]; p20=Prime[n+20]; If[PrimeQ[p0+p1+p2+p3+p4+p5+p6+p7+p8+p9+p10]&&PrimeQ[p10+p11+p12+p13+p14+p15+p16+p17+p18+p19+p20], AppendTo[lst, p10]], {n, 7!}]; lst
Select[Partition[Prime[Range[700]], 21, 1], AllTrue[{Total[Take[#, 11]], Total[Take[#, -11]]}, PrimeQ]&][[All, 11]] (* Harvey P. Dale, Sep 19 2022 *)

Crossrefs

Cf. A156781, A156782, A156783, A156784

Sequence in context: A126588 A142794 A225888 * A123043 A142014 A115163

Adjacent sequences: A156968 A156969 A156970 * A156972 A156973 A156974

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 19 2009

Status

approved