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A104157
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Smallest of n^2 consecutive primes that form an n X n magic square with the least magic constant, or 0 if no such magic square exists.
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8
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2, 0, 1480028129, 31, 13, 7, 7, 79, 37, 23, 67, 89, 13, 89, 131, 31, 71, 47, 43, 73, 277, 353, 41, 67, 127, 223, 79, 13, 193, 5, 23, 43, 5, 67, 3, 19, 5, 59, 59, 653, 19, 19, 97, 409, 5, 383, 29, 137, 379, 349, 653, 1187, 47, 41, 37, 17, 619, 89, 283, 283, 43, 479, 191
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OFFSET
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1,1
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COMMENTS
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The magic constants (= sums) are given in A073520. For a given sum, the corresponding list of primes (and thus also the smallest one) is easily calculated, cf. PARI code. - M. F. Hasler, Oct 29 2018
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REFERENCES
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H. L. Nelson, Journal of Recreational Mathematics, 1988, vol. 20:3, p. 214.
Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.
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LINKS
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FORMULA
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Conjecture: for n > 4, a(n) = prime(s) where s > 1 is the smallest integer such that (Sum_{i=s..s+n^2-1} prime(i))/n is an integer of the same parity as n. - Max Alekseyev, Jan 29 2010
a(n) = prime(i) such that Sum_{k=0..n^2-1} prime(i+k) = n*A073520(n). - M. F. Hasler, Oct 29 2018
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PROG
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(PARI) A104157(n)=MagicPrimes(A073520[n], n)[1] \\ See A073519 for MagicPrimes(). This code uses a precomputed array A073520, but in practice one would rather compute that sequence as function of this one. - M. F. Hasler, Oct 29 2018
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CROSSREFS
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Cf. A073519 or A320873 (the square for 3 X 3), A073520 (magic sums for 4 X 4 squares of consecutive primes), A073521 (consecutive primes of a 4 X 4 magic square), A073522 (consecutive primes of a (non minimal!) 5 X 5 magic square), A073523 (consecutive primes of a pandiagonal 6 X 6 magic square).
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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a(5)-a(6) corrected, a(7)-a(20) added by Max Alekseyev, Sep 24 2009
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STATUS
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approved
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