cp's OEIS Frontend

A238222 Numbers m with property that m^2 + (m+1)^2 and (m+1)^2 + (m+2)^2 are prime.

%I A238222 #23 Feb 25 2017 09:19:28
%S A238222 1,4,24,29,34,69,84,99,109,224,229,259,284,289,319,389,409,474,489,
%T A238222 494,514,589,679,694,709,749,759,844,949,1079,1099,1134,1174,1189,
%U A238222 1194,1269,1294,1304,1329,1364,1409,1474,1714,1749,1784,1844,1854,1924,2014,2059,2099,2149
%N A238222 Numbers m with property that m^2 + (m+1)^2 and (m+1)^2 + (m+2)^2 are prime.
%C A238222 Integers m such both m and m+1 are terms in A027861.
%C A238222 All corresponding primes are == 1 mod 4 (A002144 Pythagorean primes) and terms in A027862.
%C A238222 No such m such that also (m+2)^2 + (m+3)^2 is prime.
%H A238222 Zak Seidov, <a href="/A238222/b238222.txt">Table of n, a(n) for n = 1..2000</a>
%e A238222 1 is in the sequence because 1^2+2^2 = 5 and 2^2+3^2 = 13 are both prime.
%e A238222 4 is in the sequence because 4^2+5^2 = 41 and 5^2+6^2 = 61 are both prime.
%t A238222 Reap[Do[If[PrimeQ[k^2+(k+1)^2]&&PrimeQ[(k+1)^2+(k+2)^2],Sow[k]],{k,2000}]][[2,1]]
%t A238222 Select[Range[2500],AllTrue[{#^2+(#+1)^2,(#+1)^2+(#+2)^2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 25 2017 *)
%o A238222 (PARI) s=[]; for(m=1, 2500, if(isprime(m^2+(m+1)^2) && isprime((m+1)^2+(m+2)^2), s=concat(s, m))); s \\ _Colin Barker_, Feb 21 2014
%Y A238222 Cf. A002144, A062067, A027862. Subsequence of A027861.
%K A238222 nonn
%O A238222 1,2
%A A238222 _Zak Seidov_, Feb 21 2014