A174922 Lesser of twin primes p1 such that p1+(p2^2-p1^2) and p2+(p2^2-p1^2) are prime numbers.

5, 11, 29, 461, 599, 659, 809, 1019, 1289, 2027, 2141, 2309, 2339, 2801, 3329, 3557, 3581, 4127, 4421, 4547, 5879, 6761, 10091, 10457, 10709, 13829, 15329, 18911, 20231, 21839, 23561, 23909, 26249, 26879, 27581, 27689, 27917, 28109, 30491

Offset

1,1

Comments

5+(7^2-5^2)=5+24=29; 7+(7^2-5^2)=7+24=31,..

Links

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

Mathematica

lst={}; Do[p1=Prime[n]; p2=p1+2; If[PrimeQ[p2]&&PrimeQ[p1+(p2^2-p1^2)]&&PrimeQ[p2+(p2^2-p1^2)], AppendTo[lst, p1]], {n, 8!}]; lst
prQ[{a_, b_}]:=Module[{c=b^2-a^2}, AllTrue[{a+c, b+c}, PrimeQ]]; Transpose[ Select[ Select[ Partition[Prime[Range[5000]], 2, 1], #[[2]]-#[[1]] == 2&], prQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2015 *)

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A174920

Sequence in context: A358900 A337394 A090119 * A088484 A179256 A209659

Adjacent sequences: A174919 A174920 A174921 * A174923 A174924 A174925

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Status

approved