cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A270305 Magic sums of 3 X 3 magic squares composed of consecutive primes.

Original entry on oeis.org

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
Offset: 1

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Author

Arkadiusz Wesolowski, Mar 14 2016

Keywords

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

Crossrefs

Cf. A073519, A073520, A166113, A173981, A256891, A343194, A343195.
Subsequence of A268912.

Programs

  • 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

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

A270864 Magic sums of 4 X 4 semimagic squares composed of consecutive primes.

Original entry on oeis.org

124, 204, 240, 258, 276, 328, 348, 468, 1764, 1812, 2556, 3354, 5118, 5768, 5940, 8160, 8574, 11298, 16230, 16932, 19896, 23364, 24202, 32778, 37452, 37668, 39582, 44070, 44226, 45146, 50478, 51838, 58522, 65718, 72438, 84630, 86418, 86562, 103862, 105646, 114076
Offset: 1

Views

Author

Arkadiusz Wesolowski, Mar 24 2016

Keywords

Links

Crossrefs

Cf. A268912, A270865. Supersequence of A173981.

A270829 Smallest magic sum for any n X n semimagic square made from consecutive primes, or 0 if no such magic square exists.

Original entry on oeis.org

2, 0, 65573, 124, 313, 484, 797, 2016, 2211, 2862, 4507, 6188, 6325, 9660, 12669, 13016, 16857, 19530, 23069, 28184, 38761, 46302, 42515, 49846, 59087, 70260, 73385, 78960, 97267, 98316, 111023, 124454, 134641, 152952, 163043, 180596, 195975, 218432
Offset: 1

Views

Author

Arkadiusz Wesolowski, Mar 23 2016

Keywords

Comments

a(n) <= A073520(n). For n = 3 and 4, a(n) is different from A073520(n).

Links

Crossrefs

Cf. A073520, A268912, A270830.

Formula

a(2) = 0, otherwise a(n) = (1/n) * sum(m=k..n^2+k-1, A000040(m)), where k = A049084(A270830(n)).

A268913 Magic sums of 3 X 3 semimagic squares composed of primes.

Original entry on oeis.org

53, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 99, 101, 103, 107, 109, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 15 2016

Keywords

Comments

This sequence is infinite because the Green-Tao theorem implies that sequence A268790 is infinite.
I conjecture that every odd number greater than 111 belongs to this sequence.

Examples

			Examples of 3 X 3 semimagic squares composed of primes.
.
|---|---|---|
| 3 | 13| 37|
|---|---|---|
| 31| 17| 5 |
|---|---|---|
| 19| 23| 11|
|---|---|---|
The magic constant is 53 = a(1).
.
|---|---|---|
| 3 | 13| 43|
|---|---|---|
| 37| 17| 5 |
|---|---|---|
| 19| 29| 11|
|---|---|---|
The magic constant is 59 = a(2).

Links

Crossrefs

Cf. A268912. Supersequence of A268790.
Showing 1-4 of 4 results.

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