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 A256891 Smallest primes of 3 X 3 magic squares formed from consecutive primes. 12
 1480028129, 1850590057, 5196185947, 5601567187, 5757284497, 6048371029, 6151077269, 9517122259, 19052235847, 20477868319, 23813359613, 24026890159, 26748150199, 28519991387, 34821326119, 44420969909, 49285771679, 73827799009, 73974781889, 74220519319, 76483907837, 76560277009, 80143089599, 85892025227, 89132925737, 95515449037, 99977424653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let a = a(n) for some n and {a, b, c, d, e, f, g, h, i} be the set of consecutive primes. Then it is: +---+---+---+ +---+---+---+ | d | c | h | | c | d | h | +---+---+---+ +---+---+---+ | i | e | a | (type 1), or | i | e | a | (type 2). See Harvey D. Heinz. +---+---+---+ +---+---+---+ | b | g | f | | b | f | g | +---+---+---+ +---+---+---+ The type is determined by the sign of A343195. For a given magic sum S, it is easy to calculate the unique set of n^2 consecutive primes that sum up to n*S (see PROGRAM MagicPrimes() in A073519), and in particular the smallest of these (cf. PROGRAM), listed here for n = 3, in A260673 for n = 4, in A272386 for n = 5, and in A272387 for n = 6. - M. F. Hasler, Oct 28 2018 REFERENCES Allan W. Johnson, Jr., Consecutive-Prime Magic Squares, Journal of Recreational Mathematics, vol. 15, 1982-83, pp. 17-18. H. L. Nelson, A Consecutive Prime 3 x 3 Magic Square, Journal of Recreational Mathematics, vol. 20:3, 1988, p. 214. LINKS A.H.M. Smeets, Table of n, a(n) for n = 1..759 Harvey D. Heinz, Prime Numbers Magic Squares: Minimum consecutive primes - 3, 1999-2010. Eric Weisstein's World of Mathematics, Prime Magic Square Index entries for sequences related to magic squares FORMULA a(n) = A151799(A151799(A151799(A151799(A166113(n))))). - Max Alekseyev, Nov 02 2015 PROG (Magma) /* Brute-force search */ lst:=[]; n:=3; while n lt 10^11 do a:=NextPrime(n); q:=a; j:=a-n; if j mod 6 eq 0 then b:=NextPrime(a); if j eq b-a then c:=NextPrime(b); d:=c-b; if d mod 6 eq 0 then e:=NextPrime(c); k:=e-c; if k eq j then f:=NextPrime(e); if k eq f-e then g:=NextPrime(f); if g-f eq d then h:=NextPrime(g); m:=h-g; if m eq k then i:=NextPrime(h); if h-g eq i-h then Append(~lst, n); end if; end if; end if; end if; end if; end if; end if; end if; n:=q; end while; lst; (PARI) A256891(n)=MagicPrimes(A270305(n), 3)[1] \\ See A073519 for MagicPrimes(). - M. F. Hasler, Oct 28 2018 CROSSREFS Cf. A073519, A151799, A166113, A260673, A272386, A272387, A343194, A343195. Subsequence of A265139. Sequence in context: A048051 A345337 A073519 * A320873 A166113 A157816 Adjacent sequences: A256888 A256889 A256890 * A256892 A256893 A256894 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Apr 12 2015 EXTENSIONS Extended by Max Alekseyev, Nov 02 2015 STATUS approved

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Last modified December 11 14:18 EST 2023. Contains 367727 sequences. (Running on oeis4.)