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

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

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: A137980 A348299 A144137 * A180924 A366190 A176900

Adjacent sequences: A238219 A238220 A238221 * A238223 A238224 A238225

Keyword

nonn

Author

Zak Seidov, Feb 21 2014

Status

approved