A115050 Numbers k such that in the 3 X 3 square arrangement of the 9 primes p(k),..,p(k+8), totals of 3 rows and 3 columns, are all prime.

4, 8116, 12653, 12659, 53382, 114292, 142030, 161917, 198019, 376122, 417979, 450357, 606997, 764103, 958228, 966788, 1093696, 1319430, 1501073, 1943410, 2492332, 2535726, 2608633, 2680862, 2897882, 3053978, 3399460, 3433353, 3635687, 3922403, 3985059, 4495622, 4496529, 4600470

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

a(1) = 417979 because p(417979) = 6080051 and we have 3 x 3 square with desired property:
................
..7..11..13=>31.
.17..19..23=>59.
.29..31..37=>97.
..v..v...v.
.53..61..73.

Prog

(PARI) isok(v)=isprime(v[1] + v[2] + v[3]) && isprime(v[4] + v[5] + v[6]) && isprime(v[7] + v[8] + v[9]) && isprime(v[1] + v[4] + v[7]) && isprime(v[2] + v[5] + v[8]) && isprime(v[3] + v[6] + v[9])
{ my(k=1, v=primes(9)); forprime(p=nextprime(v[9]+1), 10^8, v=concat(v[2..9], p); k++; if(isok(v), print1(k, ", "))) } \\ Andrew Howroyd, Feb 13 2026

Crossrefs

Cf. A116936.

Sequence in context: A058464 A053951 A058460 * A072724 A116271 A274551

Adjacent sequences: A115047 A115048 A115049 * A115051 A115052 A115053

Keyword

nonn

Author

Zak Seidov, Feb 28 2006

Extensions

a(6) onward from Andrew Howroyd, Feb 13 2026

Status

approved