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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A339062 Sorted list of prime numbers in the union of 7-tuples (a,b,c,d,e,f,g) satisfying a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 = a*b*c*d*e*f*g.

Original entry on oeis.org

2, 3, 5, 23, 37, 67, 181, 307, 359, 1559, 2417, 59123, 88327, 95783, 99907, 304151, 606839, 932999, 1179491, 1531619, 1860337, 2188919, 2363441, 3578437, 5474849, 7577351, 11273459, 12994823, 32393057, 48222721, 127896599, 248648401, 932998067, 1109123111, 2671715093, 4488932999, 9347244311
Offset: 1

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Author

Giorgos Kalogeropoulos, Nov 22 2020

Keywords

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).

Examples

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

Links

Crossrefs

Cf. A227208, A178444.
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