A232878 Twin prime pairs which sum to perfect squares.

17, 19, 71, 73, 881, 883, 1151, 1153, 2591, 2593, 3527, 3529, 4049, 4051, 15137, 15139, 20807, 20809, 34847, 34849, 46817, 46819, 69191, 69193, 83231, 83233, 103967, 103969, 112337, 112339, 149057, 149059, 176417, 176419, 179999, 180001, 206081, 206083

Offset: 1

Author

Gary Croft, Dec 01 2013

Keywords

• nonn

Comments

All square roots of twin prime sums in this sequence (see A152786) are multiples of 6.

Digital roots of all pairs in this sequence are {8,1}.

Twin primes of the form 18n^2 +- 1. - Charles R Greathouse IV, Aug 26 2014

Examples

			17+19 = 36, square root of 36 = 6; 71+73 = 144, square root of 144 = 12.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001097, A054735, A069496, A077800.

Programs

Mathematica

t = {}; Do[ps = {2 n^2 - 1, 2 n^2 + 1}; If[PrimeQ[ps[[1]]] && PrimeQ[ps[[2]]], AppendTo[t, ps]], {n, 1000}]; Flatten[t] (* T. D. Noe, Dec 03 2013 *)

PARI

for(n=1,1e3, if(isprime(t=18*n^2-1) && isprime(t+2), print1(t", "t+2", "))) \\ Charles R Greathouse IV, Aug 26 2014

Formula

a(2*n) = a(2*n-1) + 2, a(2*n+1) = A069496(n).