cp's OEIS Frontend

A244807 The hexagonal spiral of Champernowne, read along the East (or 90-degree) ray.

%I A244807 #24 Jul 29 2023 04:07:15
%S A244807 1,2,9,1,5,3,3,7,3,1,3,0,1,9,3,2,8,4,3,8,3,4,0,0,5,4,5,7,0,8,9,7,9,1,
%T A244807 7,1,1,1,1,1,7,1,9,1,7,1,1,1,1,2,7,2,9,2,7,2,1,2,1,2,7,3,9,3,7,3,1,3,
%U A244807 1,3,7,4,9,4,7,4,1,4,1,4,7,5,9,5,7,5,1,5,1,6,7,6,9,6,7,6,1,7,1,7,7,7,9,8,7
%N A244807 The hexagonal spiral of Champernowne, read along the East (or 90-degree) ray.
%C A244807 Inspired by Stanislaw M. Ulam's hexagonal spiral, circa 1963. See example section of A056105.
%C A244807 When A056105, A056106, A056107, A056108, A056109 & A003215 were submitted, the offsets were 0. Here the offset is 1.
%F A244807 For each 30 degrees of the compass, the corresponding spoke (or ray) has a generating formula as follows:
%F A244807    090:  3n^2- 8n +6
%F A244807    060: 12n^2-27n+16
%F A244807    030:  3n^2- 7n+ 5
%F A244807    000: 12n^2-25n+14
%F A244807    330:  3n^2 -6n +4
%F A244807    300: 12n^2-23n+12
%F A244807    270:  3n^2 -5n +3
%F A244807    240: 12n^2-21n+10
%F A244807    210:  3n^2 -4n +2
%F A244807    180: 12n^2-19n +8
%F A244807    150:  3n^2 -3n +1
%F A244807    120: 12n^2-17n+ 6
%F A244807 Also see formula section of A056105.
%e A244807 .
%e A244807 ..................7...5...1...6...5...1...5...5...1...4
%e A244807 .
%e A244807 ................1...6...3...1...5...3...1...4...3...1...3
%e A244807 .
%e A244807 ..............3...1...7...1...1...6...1...1...5...1...1...3
%e A244807 .
%e A244807 ............7...1...1...0...0...1...9...9...8...9...7...4...1
%e A244807 .
%e A244807 ..........1...8...0...7...8...7...7...7...6...7...5...9...1...2
%e A244807 .
%e A244807 ........3...1...1...9...9...5...8...5...7...5...6...7...6...1...3
%e A244807 .
%e A244807 ......8...1...1...8...6...4...2...4...1...4...0...5...4...9...3...1
%e A244807 .
%e A244807 ....1...9...0...0...0...3...9...2...8...2...7...4...5...7...5...1...1
%e A244807 .
%e A244807 ..3...1...2...8...6...4...3...1...8...1...7...2...9...5...3...9...1...3
%e A244807 .
%e A244807 9...2...1...1...1...4...0...9...1...1...0...1...6...3...4...7...4...2...1
%e A244807 .
%e A244807 ..0...0...8...6...4...3...2...1...4...3...1...6...2...8...5...2...9...1...0
%e A244807 .
%e A244807 1...3...2...2...5...1...0...2...5...1...2...9...1...5...3...3...7...3...1...3
%e A244807 .
%e A244807 ..2...1...8...6...4...3...2...1...6...7...8...5...2...7...5...1...9...1...1
%e A244807 .
%e A244807 ....1...0...3...3...6...2...1...3...1...4...1...4...3...2...7...2...1...9
%e A244807 .
%e A244807 ......1...4...8...6...4...3...2...2...2...3...2...6...5...0...9...1...2
%e A244807 .
%e A244807 ........2...1...4...4...7...3...3...4...3...5...3...1...7...1...0...1
%e A244807 .
%e A244807 ..........2...0...8...6...4...8...4...9...5...0...5...9...9...1...8
%e A244807 .
%e A244807 ............1...5...5...5...6...6...6...7...6...8...6...0...1...2
%e A244807 .
%e A244807 ..............2...1...8...6...8...7...8...8...8...9...9...9...1
%e A244807 .
%e A244807 ................3...0...6...1...0...7...1...0...8...1...0...7
%e A244807 .
%e A244807 ..................1...2...4...1...2...5...1...2...6...1...2
%e A244807 .
%e A244807 ....................1...4...4...1...4...5...1...4...6...1
%e A244807 .
%t A244807 almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]];
%t A244807 f[n_] := 3n^2- 8n +6 (* see formula section of A244807 *); Array[ almostNatural[ f@#, 10] &, 105]
%Y A244807 Cf. A007376, A054552, A056105, A244808, A244809, A244810, A244811, A244812, A244813, A244814, A244815, A244816, A244817, A244818.
%K A244807 nonn,base,easy
%O A244807 1,2
%A A244807 _Robert G. Wilson v_, Jul 06 2014