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 A139775 Primes p2 such that p1^2 + p2^3 and p1^3 + p2^2 are averages of twin primes. p1 and p2 consecutive primes, p1 < p2. 1
 29, 210071, 10480889, 10526501, 11210333, 11722901, 12252269, 12334121, 13647089, 15550421, 23652539, 26724479, 31165139, 48668111, 50599841, 51412019, 56699039, 80672393, 82804769, 90962141, 104066489, 109197419, 109953803, 120560879, 127503119, 153189503, 161933327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..1200 EXAMPLE p2 = 29 is a term since the previous prime is p1 = 23, and both p1^2 + p2^3 = 24918 and p1^3 + p2^2 = 13008 are averages of twin primes. MATHEMATICA a={}; Do[p1=Prime[n]; p2=Prime[n+1]; p3=p1^2+p2^3; p4=p1^3+p2^2; If[PrimeQ[p3-1]&&PrimeQ[p3+1]&&PrimeQ[p4-1]&&PrimeQ[p4+1], AppendTo[a, p2]], {n, 13^5}]; Print[a]; chkQ[{a_, b_}]:=Module[{c=a^2+b^3, d=a^3+b^2}, AllTrue[{c+1, c-1, d+1, d-1}, PrimeQ]]; Transpose[Select[Partition[ Prime[Range[ 3000000]], 2, 1], chkQ]][[2]] (* The program uses the AllTrue function from Mathematica version 10. *) (* Harvey P. Dale, Nov 25 2014 *) CROSSREFS Cf. A001097, A001359, A006512, A014574, A138763. Sequence in context: A343451 A185822 A321666 * A303734 A087528 A307622 Adjacent sequences: A139772 A139773 A139774 * A139776 A139777 A139778 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, May 16 2008 EXTENSIONS More terms from Harvey P. Dale, Nov 25 2014 More terms from Amiram Eldar, Jan 02 2020 STATUS approved

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Last modified June 20 23:18 EDT 2024. Contains 373535 sequences. (Running on oeis4.)