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A232878 Twin prime pairs which sum to perfect squares. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

Gary W. Croft, Perfect Twin Primes

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A001097, A054735, A069496, A077800.

Sequence in context: A075432 A232882 A119768 * A226681 A005808 A180559

Adjacent sequences:  A232875 A232876 A232877 * A232879 A232880 A232881

KEYWORD

nonn

AUTHOR

Gary Croft, Dec 01 2013

STATUS

approved

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Last modified June 24 05:50 EDT 2017. Contains 288697 sequences.