cp's OEIS Frontend

A344660 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that each term, when written with one digit per square, forms no prime value in the eight sums when each digit is added to each of its eight nearest neighbors.

%I A344660 #24 Jun 01 2021 19:17:49
%S A344660 0,1,8,80,4,6,88,7,77,2,24,40,44,22,26,27,3,5,9,72,28,42,46,48,62,64,
%T A344660 66,68,87,13,31,37,78,82,84,86,60,400,422,222,63,601,73,33,15,35,17,
%U A344660 10,18,224,226,404,406,424,227,286,36,99,39,19,53,55,57,59,90,93,772,228,240,408,440,426
%N A344660 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that each term, when written with one digit per square, forms no prime value in the eight sums when each digit is added to each of its eight nearest neighbors.
%C A344660 Terms are broken into digits before entering the spiral.
%C A344660 The sequence is finite. After 181 terms (and 466 digits) the number 101 is entered. The next square is surrounded by digits 0,1,8 so the only available digit is 8. As 8 has already appeared in the sequence another digit must be added to form a new number, but the next square is now surrounded with digits 0,1,3,8, and it is not possible to find a digit such that its sum with each of those digits is not prime.
%C A344660 .
%C A344660             4---0---4---6---2---2---4---2---2---8---1
%C A344660             |                                       |
%C A344660             4   4---0---6---6---8---4---8---2---8   0
%C A344660             |   |                               |   |
%C A344660             .   0   4---6---4---2---4---8---2   8   1
%C A344660             .   |   |                       |   |   |
%C A344660             .   0   8   0---4---4---2---2   2   7   7
%C A344660             .   |   |   |               |   |   |   |
%C A344660             .   4   6   4   0---8---8   7   7   7   1
%C A344660             .   |   |   |   |       |   |   |   |   |
%C A344660             .   2   2   4   4   0---1   7   9   3   5
%C A344660             .   |   |   |   |           |   |   |   |
%C A344660             .   2   6   2   6---8---8---7   5   1   3
%C A344660             .   |   |   |                   |   |   |
%C A344660             .   2   4   2---2---6---2---7---3   3   5
%C A344660             .   |   |                           |   |
%C A344660             .   2   6---6---6---8---8---7---1---3   1
%C A344660             .   |                                   |
%C A344660             .   2---6---3---6---0---1---7---3---3---3
%C A344660 .
%e A344660 The eight digits that are in contact with the initial zero are 1, 8, 8, 0, 4, 6, 8, 8: none of them is prime [forcing the sum a(k) + 0 to be nonprime, with k<9]; more generally, no term of the square spiral added to any of its eight nearest neighbors sums to a prime.
%Y A344660 Cf. A063826, A344659, A002808, A000040.
%K A344660 base,nonn,fini
%O A344660 1,3
%A A344660 _Eric Angelini_ and _Scott R. Shannon_, May 26 2021