A126118 Primes of the form a^2 + b^2 + c^2 such that a^4 + b^4 + c^4 is prime as well and larger than the first one.

101, 107, 149, 173, 179, 251, 389, 521, 701, 1097, 1601, 1613, 1901, 1907, 2549, 2897, 2909, 3701, 4133, 4139, 5051, 6101, 7229, 7817, 7829, 8429, 10457, 11171, 11933, 12689, 13499, 15131, 15149, 16883, 18749, 19697, 20693, 21701, 22721, 22739

Offset

1,1

Comments

With a=b=1 and c=0, both a^2 + b^2 + c^2 and a^4 + b^4 + c^4 would yield 2 (a prime); similarly, with a=b=c=1, both sums would yield 3 (also a prime). Thus, without the "larger than the first one" constraint, both 2 and 3 would be terms of this sequence. - Jon E. Schoenfield, Jun 15 2021

Links

Table of n, a(n) for n=1..40.

Example

101 = 1^2 + 6^2 + 8^2 and 5393 = 1^4 + 6^4 + 8^4 is prime as well.
31859 = 99^2 + 103^2 + 107^2 and 339690083 = 99^4 + 103^4 + 107^4 is prime as well.

Crossrefs

Sequence in context: A111348 A081649 A344802 * A118773 A092628 A107219

Adjacent sequences: A126115 A126116 A126117 * A126119 A126120 A126121

Keyword

nonn

Author

Tomas Xordan, Mar 05 2007

Status

approved