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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: A132239 A075432 A232882 * 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 March 29 04:13 EDT 2020. Contains 333105 sequences. (Running on oeis4.)