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#31 by Susanna Cuyler at Sun Oct 28 09:11:46 EDT 2018
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#30 by M. F. Hasler at Sun Oct 28 02:44:59 EDT 2018
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#29 by M. F. Hasler at Sun Oct 28 02:44:38 EDT 2018
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(PARI) A073519=MagicPrimes(4440084513, 3) \\ where :: (also used in A073521, ...)
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proposed
editing
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#28 by M. F. Hasler at Sun Oct 28 02:42:14 EDT 2018
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Discussion
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| Sun Oct 28
| 02:42
| M. F. Hasler: (Thanks!)
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#27 by M. F. Hasler at Sun Oct 28 02:40:51 EDT 2018
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AThe set of nine consecutive primes forming a 3 X 3 magic square with the smallest magic constant (4440084513).
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Discussion
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| Sun Oct 28
| 02:42
| M. F. Hasler: Yes to both. Fixed.
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#26 by M. F. Hasler at Sun Oct 28 02:40:29 EDT 2018
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The square is given (with the terms in correct order) in A320873. The (increasingly ordered) set of primes does not contain more information than the magic constant (= sum) S, since they have to be consecutive and sum up to 3*S. It is easy to construct the unique set of (consecutive) primes with this property, cf. PROGRAM.. - _M. F. Hasler_, Oct 28 2018
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proposed
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#25 by M. F. Hasler at Sun Oct 28 00:27:52 EDT 2018
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Discussion
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| Sun Oct 28
| 02:32
| Michel Marcus: The set like in A073521 ? you forgot to sign comment ?
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| 02:32
| Michel Marcus: The set like in A073521 ? you forgot to sign comment ?
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#24 by M. F. Hasler at Sun Oct 28 00:26:58 EDT 2018
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| COMMENTS
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The square is given (with the terms in correct order) in A320873. The (increasingly ordered) set of primes does not contain more information than the magic constant (= sum) S, since they have to be consecutive and sum up to 3*S. It is easy to construct the unique set of (consecutive) primes with this property, cf. PROGRAM.
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(PARI) A073519=MagicPrimes(4440084513, 3) \\ where :
(PARI) A073519MagicPrimes(S=4440084513, n=3, P=[nextprime(S\n)])={S=n*S-P[1]; for(i=1, -1+n*=n, S-=if(S>(n-i)*P[1], P=concat(P, nextprime(P[#P]+1)); P[#P], P=concat(precprime(P[1]-1), P); P[1])); if(S, -P, P)} \\ The vector of n^2 primes whose sum is n*S (= this seq. for default values), , or a negative vector with an approximate solution if no exact solution exists. - M. F. Hasler, Oct 22 2018
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#23 by M. F. Hasler at Mon Oct 22 21:03:22 EDT 2018
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(PARI) A073519(S=4440084513, n=3, P=[nextprime(S\n)])={S=n*S-P[1]; for(i=1, -1+n*=n, S-=if(S>(n-i)*P[1], P=concat(P, nextprime(P[#P]+1)); P[#P], P=concat(precprime(P[1]-1), P); P[1])); if(S, -P, P)} \\ The vector of n^2 primes whose sum is n*S (= this seq. for default values), or a negative vector with an approximate solution if no exact solution exists. - . - _M. F. Hasler, _, Oct 22 2018
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#22 by M. F. Hasler at Mon Oct 22 21:00:47 EDT 2018
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(PARI) A073519(S=4440084513, n=3, P=[nextprime(S\n)])={S=n*S-P[1]; for(i=1, -1+n*=n, S-=if(S>(n-i)*P[1], P=concat(P, nextprime(P[#P]+1)); P[#P], P=concat(precprime(P[1]-1), P); P[1])); if(S, -P, P)} \\ The vector of n^2 primes whose sum is n*S (= this seq. for default values), or a negative vector with an approximate solution if no exact solution exists. - M. F. Hasler, Oct 22 2018
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approved
editing
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