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 A302659 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, A065368(a(n) * a(n+1)) = 0. 1
 1, 4, 2, 6, 8, 3, 12, 7, 16, 5, 24, 9, 28, 10, 14, 18, 20, 11, 32, 15, 44, 13, 36, 17, 40, 19, 52, 21, 48, 22, 26, 30, 34, 38, 42, 46, 50, 56, 23, 60, 25, 64, 27, 68, 29, 72, 31, 76, 35, 80, 33, 84, 37, 88, 41, 96, 43, 92, 39, 100, 45, 112, 47, 116, 49, 104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For any base b > 1: - let s_b be the alternate sum of digits in base b, - in particular s_2 = A065359, s_3 = A065368 and s_10 = A225693, - we can build an analog of this sequence, say f_b, by considering s_b instead of A065368, - f_b is well defined: for any k > 0, s_b(k * (1 + b^(2*i + 1))) = 0 whenever k < b^(2*i + 1), hence we can always extend the sequence, - f_b is conjectured to be a permutation of the natural numbers, - the scatterplot of f_b shows lines that seem related to the value of s_b(f_b) mod b+1. See A302544 for a similar sequence. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, Colored scatterplot of the first 10000 terms Rémy Sigrist, Scatterplot of the first 10000 of f_2 Rémy Sigrist, Scatterplot of the first 10000 of f_5 Rémy Sigrist, PARI program for A302659 Index entries for sequences related to digital root, sum, etc. EXAMPLE The first terms, alongside the ternary representation of a(n) * a(n+1), are: n a(n) tern(a(n) * a(n+1)) -- ---- ------------------- 1 1 11 2 4 22 3 2 110 4 6 1210 5 8 220 6 3 1100 7 12 10010 8 7 11011 9 16 2222 10 5 11110 11 24 22000 12 9 100100 PROG (PARI) See Links section. CROSSREFS Cf. A065359, A065368, A225693, A302544. Sequence in context: A114478 A367882 A330530 * A363705 A134239 A136390 Adjacent sequences: A302656 A302657 A302658 * A302660 A302661 A302662 KEYWORD nonn,base AUTHOR Rémy Sigrist, Apr 11 2018 STATUS approved

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Last modified June 23 10:25 EDT 2024. Contains 373629 sequences. (Running on oeis4.)