

A238222


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


1



1, 4, 24, 29, 34, 69, 84, 99, 109, 224, 229, 259, 284, 289, 319, 389, 409, 474, 489, 494, 514, 589, 679, 694, 709, 749, 759, 844, 949, 1079, 1099, 1134, 1174, 1189, 1194, 1269, 1294, 1304, 1329, 1364, 1409, 1474, 1714, 1749, 1784, 1844, 1854, 1924, 2014, 2059, 2099, 2149
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OFFSET

1,2


COMMENTS

Integers m such both m and m+1 are terms in A027861.
All corresponding primes are == 1 mod 4 (A002144 Pythagorean primes) and terms in A027862.
No such m such that also (m+2)^2 + (m+3)^2 is prime.


LINKS

Zak Seidov, Table of n, a(n) for n = 1..2000


EXAMPLE

1 is in the sequence because 1^2+2^2 = 5 and 2^2+3^2 = 13 are both prime.
4 is in the sequence because 4^2+5^2 = 41 and 5^2+6^2 = 61 are both prime.


MATHEMATICA

Reap[Do[If[PrimeQ[k^2+(k+1)^2]&&PrimeQ[(k+1)^2+(k+2)^2], Sow[k]], {k, 2000}]][[2, 1]]
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 *)


PROG

(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


CROSSREFS

Cf. A002144, A062067, A027862. Subsequence of A027861.
Sequence in context: A324517 A137980 A144137 * A180924 A176900 A166727
Adjacent sequences: A238219 A238220 A238221 * A238223 A238224 A238225


KEYWORD

nonn


AUTHOR

Zak Seidov, Feb 21 2014


STATUS

approved



