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A283391 Primes p such that a^2 + b^2 = p^2 and q = a + b is prime, where a,b > 0. 3
5, 13, 17, 29, 37, 53, 61, 73, 97, 109, 113, 137, 149, 181, 193, 197, 229, 233, 277, 293, 313, 317, 337, 349, 401, 421, 449, 457, 461, 521, 541, 569, 613, 641, 653, 673, 677, 701, 709, 757, 809, 821, 853, 877, 929, 941, 977, 997, 1009, 1021, 1049, 1061, 1069, 1093, 1117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p = x^2 + y^2 such that q = x^2 - y^2 + 2*x*y is prime, where x > y > 0.

Primes q are 7, 17, 23, 41, 47, 73, 71, 103, 137, 151, 127, 193, 191, ...

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

MATHEMATICA

Select[Prime@ Range@ 200, Length@ Select[PowersRepresentations[#^2, 2, 2], PrimeQ@ Total@ # &] > 1 &] (* Michael De Vlieger, Mar 07 2017 *)

PROG

(PARI) T=thueinit('x^2+1, 1);

is(n)=if(n%4 != 1 || !isprime(n), return(0)); my(v=thue(T, n^2)); for(i=1, #v, if(v[i][1]>0 && v[i][2]>=v[i][1] && isprime(vecsum(v[i])), return(1))); 0 \\ Charles R Greathouse IV, Mar 07 2017

CROSSREFS

Subsequence of A002144.

Sequence in context: A192592 A111055 A307096 * A145016 A123079 A273950

Adjacent sequences:  A283388 A283389 A283390 * A283392 A283393 A283394

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Mar 07 2017

EXTENSIONS

More terms from Altug Alkan, Mar 07 2017

STATUS

approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)