A154676 Numbers n = 103*k^2 such that (n-1,n+1) is a twin prime pair (thus k = 6*m).

2317500, 12047292, 26163648, 43250112, 47347452, 61704828, 168228252, 333720000, 351755712, 426127068, 513127872, 840143808, 979638768, 998790588, 1089276912, 1330434108, 1357220700, 1388809152, 1694467008, 1927570428, 1986835392, 2035992348, 2136108348, 2858437872, 3070594800, 3241626300, 3903322608

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Keywords

• nonn
• less

Comments

Original definition: Averages of twin prime pairs n such that n*103 and n/103 are squares.

All terms are of the form 3708*k^2. - Zak Seidov, Jan 15 2009

Obviously n*103 is a square iff n/103 is a square, say k^2. But n=103k^2 can't be the average of a twin prime pair unless it's a multiple of 6, thus k=6m and n=103*36*m^2. - M. F. Hasler, Apr 11 2009

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A154670, A154671, A154672, A154673, A154674, A154675.

Programs

Maple

select(t -> isprime(t+1) and isprime(t-1), [seq(3708*i^2, i=1..2000)]); # Robert Israel, Mar 13 2019

Mathematica

lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*103)^(1/2); If[Floor[s]==s,AppendTo[lst,n]]],{n,9!,2*11!,6}]; lst (*...and/or...*) lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/103)^(1/2); If[Floor[s]==s,AppendTo[lst,n]]],{n,9!,2*11!,6}]; lst
Select[3708*Range[1200]^2,AllTrue[#+{1,-1},PrimeQ]&] (* Harvey P. Dale, May 15 2025 *)

PARI

forstep(k=0,1e4,6, isprime(k^2*103+1) & isprime(k^2*103-1) & print1(k^2*103,",")) \\ M. F. Hasler, Apr 11 2009

Extensions

Edited and extended by M. F. Hasler, Apr 11 2009