OFFSET

1,1

COMMENTS

Prime numbers that appear in the integer solutions {X(1),X(2),...X(n)} of Markoff-Hurwitz equation X(1)^2 + ... + X(n)^2 = a*X(1)*...*X(n) for a=1 and n=7.

7-tuples that are solutions of the above equation consisting only of primes appear to be very rare. In this special case the number N=X(1)*...*X(7) is equal to the sum of the squares of its prime factors (with multiplicity).

Giorgos Kalogeropoulos has found two numbers N having 123 and 163 digits respectively.

The factors of the first one are {2, 2, 2, 23, 1109123111, 57766182616657495290612267717977498812931942308391, 11788844704086155814066994795339207139099517865226893357415731}, so this 7-tuple is a solution and all these primes belong to the sequence. (See Rivera's link for the second 7-tuple).

LINKS

Carlos Rivera, Puzzle 1019. Follow-up to Puzzle 625, The Prime Puzzles and Problems Connection.

EXAMPLE

{1, 1, 2, 2, 3, 23, 274} is a solution to the equation. So the primes 2,3,23 are terms of the sequence.

CROSSREFS

KEYWORD

nonn

AUTHOR

Giorgos Kalogeropoulos, Nov 22 2020

STATUS

approved