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 A354441 Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3X3 square of numbers sums to a prime. 8
 1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 10, 13, 12, 14, 20, 16, 15, 17, 19, 22, 18, 21, 25, 26, 35, 23, 24, 27, 28, 30, 29, 31, 33, 37, 41, 36, 32, 34, 43, 38, 40, 52, 39, 42, 66, 48, 45, 44, 46, 47, 49, 54, 50, 56, 51, 57, 53, 55, 61, 72, 67, 59, 58, 62, 60, 63, 71, 68, 74, 76, 70, 80, 64, 65, 69, 77, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A354442 for the successive prime sums formed by each completed 3X3 square of numbers. LINKS Table of n, a(n) for n=1..77. Scott R. Shannon, Image of the first 4000 terms. The green line is y = n. EXAMPLE The spiral begins . . 32--36--41--37--33--31--29 57 | | | 34 15--16--20--14--12 30 51 | | | | | 43 17 5---4---3 13 28 56 | | | | | | | 38 19 6 1---2 10 27 50 | | | | | | 40 22 7---8--11---9 24 54 | | | | 52 18--21--25--26--35--23 49 | | 39--42--66--48--45--44--46--47 . . a(9) = 11 as this completes a 3X3 square of numbers 5,4,3,6,1,2,7,8,11, which sum to 47, a prime, and 11 is the smallest unused number to form a prime sum. a(12) = 13 as this completes a 3X3 square of numbers 8,11,9,1,2,10,4,3,13, which sum to 61, a prime, and 13 is the smallest unused number to form a prime sum. CROSSREFS Cf. A354442, A337116, A257339, A354434, A000040. Sequence in context: A087027 A358142 A280770 * A354435 A358277 A361513 Adjacent sequences: A354438 A354439 A354440 * A354442 A354443 A354444 KEYWORD nonn AUTHOR Scott R. Shannon, May 29 2022 STATUS approved

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Last modified September 26 19:16 EDT 2023. Contains 365666 sequences. (Running on oeis4.)