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A174922 Lesser of twin primes p1 such that p1+(p2^2-p1^2) and p2+(p2^2-p1^2) are prime numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A234511 A053185 A090119 * A088484 A179256 A209659

Adjacent sequences:  A174919 A174920 A174921 * A174923 A174924 A174925

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)