The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A138763 Primes p1 such that p1^2 + p2^3 and p1^3 + p2^2 are averages of twin primes. p1 and p2 are consecutive primes, p1 < p2. 3
 23, 210053, 10480853, 10526459, 11210321, 11722871, 12252263, 12334109, 13647083, 15550331, 23652479, 26724461, 31165133, 48668099, 50599823, 51411989, 56699033, 80672369, 82804763, 90962111, 104066441, 109197401, 109953791, 120560861, 127503113, 153189479, 161933297 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..120 EXAMPLE p1 = 23 is a term since the next prime is p2 = 29, 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, p1]], {n, 13^5}]; Print[a]; cpQ[{a_, b_}]:=Module[{p3=a^2+b^3, p4=a^3+b^2}, AllTrue[{p3+1, p3-1, p4+1, p4-1}, PrimeQ]]; Transpose[Select[Partition[Prime[ Range[ 2*10^6]], 2, 1], cpQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 11 2015 *) PROG (MAGMA) [p:p in PrimesInInterval(1, 11000000)|  IsPrime(a+1) and IsPrime(a-1) and IsPrime(b+1) and IsPrime(b-1) where a is p^2+q^3 where b is p^3+q^2  where q is NextPrime(p)]; // Marius A. Burtea, Jan 01 2020 CROSSREFS Cf. A001097, A001359, A006512, A014574. Sequence in context: A101699 A122148 A068736 * A156176 A013772 A320442 Adjacent sequences:  A138760 A138761 A138762 * A138764 A138765 A138766 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, May 15 2008 EXTENSIONS More terms from Harvey P. Dale, May 11 201 More terms from Amiram Eldar, Jan 01 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 8 09:21 EDT 2021. Contains 343666 sequences. (Running on oeis4.)