A153375 Larger of two consecutive prime numbers such that p0+p1=average of twin prime pairs and p0*p1+7=average of twin prime pairs.

7, 17, 1049, 2767, 3347, 22391, 45989, 88237, 92333, 135241, 154157, 233327, 287159, 344231, 365297, 392737, 479639, 549749, 574367, 650591, 659437, 666089, 749807, 786959, 869069, 959737, 1023541, 1045043, 1161851, 1180427, 1193041

Offset

1,1

Comments

5+7=12+-1=primes, 5*7+7=42+-1=primes; 13+17=30+-1=primes, 13*17+7=228+-1=primes;...

Links

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

Mathematica

lst={}; Do[p0=Prime[n]; p1=Prime[n+1]; a=p0+p1; b=p0*p1+7; If[PrimeQ[a-1]&&PrimeQ[a+1]&&PrimeQ[b-1]&&PrimeQ[b+1], AppendTo[lst, p1]], {n, 9!}]; lst
atpQ[{a_, b_}]:=Module[{t=a+b, p=a*b}, AllTrue[{t-1, t+1, p+6, p+8}, PrimeQ]]; Transpose[ Select[Partition[Prime[Range[100000]], 2, 1], atpQ]][[2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 09 2014 *)

Crossrefs

Cf. A099349, A153374

Sequence in context: A113765 A269447 A013540 * A001145 A093139 A177366

Adjacent sequences: A153372 A153373 A153374 * A153376 A153377 A153378

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 24 2008

Status

approved