cp's OEIS Frontend

A337116 Spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the four integers forming any 2 X 2 square add up to a prime.

%I A337116 #31 Aug 30 2020 02:29:47
%S A337116 0,1,2,4,3,6,5,8,10,7,11,9,12,14,17,13,15,16,18,24,19,23,25,28,22,20,
%T A337116 30,31,32,26,21,38,33,37,34,27,29,36,40,35,50,44,39,47,42,41,43,46,49,
%U A337116 45,53,48,54,56,59,51,52,55,65,57,64,58,60,63,61,70,62,73,75,67
%N A337116 Spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the four integers forming any 2 X 2 square add up to a prime.
%C A337116 This is (by definition) the lexicographically earliest permutation of the nonnegative integers with this property.
%H A337116 Jean-Marc Falcoz, <a href="/A337116/b337116.txt">Table of n, a(n) for n = 1..2757</a>
%e A337116 The four integers inside each of the four 2 X 2 squares that contain 0 sum up to a prime: 0+1+2+4=7 / 0+4+3+6=13 / 0+6+5+8=19 / 0+8+10+1=19. This is true for any 2 X 2 square picked up on the (infinite) grid: the upper right corner below sums up to the prime 79 for instance (22+20+30+7).
%e A337116 .
%e A337116      19--23--25--28--22--20
%e A337116       |                   |
%e A337116      24   5---8--10---7  30
%e A337116       |   |           |   .
%e A337116      18   6   0---1  11   .
%e A337116       |   |       |   |   .
%e A337116      16   3---4---2   9   .
%e A337116       |               |
%e A337116      15--13--17--14--12
%e A337116 .
%Y A337116 Cf. A214176, A337115 (same idea, with squares instead of primes), A337117 (with palindromes instead of primes), A337368 (with pandigitals).
%K A337116 nonn
%O A337116 1,3
%A A337116 _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 16 2020