A338644 Square spiral of smallest distinct positive integers starting at 1 such that the four sums of each term with its four nearest neighbors is a prime number.

1, 2, 3, 4, 7, 6, 5, 12, 11, 8, 9, 10, 13, 16, 15, 22, 19, 24, 17, 14, 23, 18, 25, 36, 35, 26, 21, 20, 27, 34, 33, 28, 31, 52, 37, 42, 29, 54, 43, 30, 53, 44, 39, 50, 89, 48, 61, 66, 41, 32, 47, 62, 51, 46, 55, 76, 63, 38, 45, 58, 49, 60, 67, 72, 59, 68, 83, 84, 73, 78, 95, 98, 65, 74, 57, 92

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Example

The square spiral starts:
.
     29--42--37--52--31--28--33
      |                       |
     54  19--22--15--16--13  34
      |   |               |   |
     43  24   7---4---3  10  27
      |   |   |       |   |   |
     30  17   6   1---2   9  20
      |   |   |           |   |
     53  14   5--12--11---8  21
      |   |                   |
     44  23--18--25--36--35--26
      |
     39--50--89--48--61--66--41..
.
a(2) = 2 as a(1) + 2 = 1 + 2 = 3, the smallest possible prime number.
a(3) = 3 as a(2) + 3 = 2 + 3 = 5, the next smallest possible prime number.
a(5) = 7 as a(4) + 7 = 4 + 7 = 11. Note a(5) cannot be 5 or 6 as when these are added to 4 the result is a composite number.
a(9) = 11 as a(8) + 11 = 12 + 11 = 23, and a(2) + 11 = 2 + 11 = 13, both being prime.

Crossrefs

Cf. A338642 (sum to composites), A000040, A063826, A260643, A334742, A307834, A338221.

Sequence in context: A297441 A292959 A292957 * A132075 A265364 A265363

Adjacent sequences: A338641 A338642 A338643 * A338645 A338646 A338647

Keyword

nonn

Author

Scott R. Shannon and Eric Angelini, Apr 21 2021

Status

approved