A270305 - OEIS

A270305

Magic sums of 3 X 3 magic squares composed of consecutive primes.

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

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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

A.H.M. Smeets, Table of n, a(n) for n = 1..759

Eric Weisstein's World of Mathematics, Prime Magic Square

Index entries for sequences related to magic squares

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

Cf. A073519, A073520, A166113, A173981, A256891, A343194, A343195.

Subsequence of A268912.

Sequence in context: A114670 A092776 A271446 * A286817 A280182 A034916

Adjacent sequences: A270302 A270303 A270304 * A270306 A270307 A270308

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Mar 14 2016

STATUS

approved