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A270305 Magic sums of 3 X 3 magic squares composed of consecutive primes. 10
4440084513, 5551770297, 15588557967, 16804701687, 17271853617, 18145113213, 18453231933, 28551366903, 57156707667, 61433605083, 71440079091, 72080670603, 80244450939, 85559974287, 104463978483, 133262909853, 147857315253, 221483397153, 221924345793, 222661558173, 229451723637, 229680831153, 240429269013, 257676075807, 267398777427, 286546347237, 299932274193 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
Eric Weisstein's World of Mathematics, Prime Magic Square
FORMULA
a(n) = 3*A166113(n).
a(n) = Sum_{k=0..8} prime(pi(A256891(n))+k)/3, where (prime)pi = A000720, prime = A000040. A similar formula is possible using the central prime A166113(n). - M. F. Hasler, Oct 28 2018
a(n) = 3*A256891(n) + 9*A343194(n) + 3*A343195(n). - A.H.M. Smeets, Apr 08 2021
PROG
(PARI) A270305(n, p=A256891[n], N=3)=sum(i=2, N^2, p=nextprime(p+1), p)/N \\ Illustrates the second formula. Uses a precomputed array A256891, unless the smallest prime is supplied as optional 2nd argument. See also the 4x4 and 5x5 analog, A173981 and A176571, where this is useful for finding possible sets of primes, cf. A260673 and A272386. - M. F. Hasler, Oct 28 2018
CROSSREFS
Subsequence of A268912.
Sequence in context: A114670 A092776 A271446 * A286817 A280182 A034916
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 09:28 EDT 2024. Contains 371268 sequences. (Running on oeis4.)