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 A162320 Array read by antidiagonals: a(n,m) = the number of digits of m when written in base n. The top row is the number of digits for each m in base 2. 2
 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 2, 4, 1, 1, 1, 1, 1, 2, 2, 2, 4, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A162319 is the same array with the lengths of base 1 numbers in the top row. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10296 (Covers bases n = 1..144) EXAMPLE From Michael De Vlieger, Jan 02 2015: (Start) Array read by antidiagonals begins: 1; 1, 2; 1, 1, 2; 1, 1, 2, 3; 1, 1, 1, 2, 3; 1, 1, 1, 2, 2, 3; 1, 1, 1, 1, 2, 2, 3; 1, 1, 1, 1, 2, 2, 2, 4; 1, 1, 1, 1, 1, 2, 2, 2, 4; ... Array adjusted such that the rows represent base n and the columns m: m 1 2 3 4 5 6 7 8 9 10 ------------------------------ base 2: 1, 2, 2, 3, 3, 3, 3, 4, 4, (4); base 3: 1, 1, 2, 2, 2, 2, 2, 2, (3, 3); base 4: 1, 1, 1, 2, 2, 2, 2, (2, 2, 2); base 5: 1, 1, 1, 1, 2, 2, (2, 2, 2, 2); base 6: 1, 1, 1, 1, 1, (2, 2, 2, 2, 2); base 7: 1, 1, 1, 1, (1, 1, 2, 2, 2, 2); base 8: 1, 1, 1, (1, 1, 1, 1, 2, 2, 2); base 9: 1, 1, (1, 1, 1, 1, 1, 1, 2, 2); base 10: 1, (1, 1, 1, 1, 1, 1, 1, 1, 1); ... For n = 12, a(12) is found in the second position in row 5 in the array read by antidiagonals. This equates to m = 2, base n = 5. The number m = 2 in base n = 5 requires 1 digit, thus a(12) = 1. For n = 20, a(20) is found in the fifth position in row 6 in the array read by antidiagonals. This equates to m = 5, base n = 3. The number m = 5 in base n = 3 requires 2 digits, thus a(20) = 2. (End) MATHEMATICA a162320[n_] := Block[{t = {}, i, j}, For[i = 1, i <= n, i++, For[j = i, j > 1, j--, AppendTo[t, Floor@Log[j, i - j + 1] + 1]]]; t]]; a162320[14] (* Michael De Vlieger, Jan 02 2015 *) CROSSREFS Cf. A162319. Sequence in context: A104368 A218878 A240061 * A241911 A335221 A136610 Adjacent sequences: A162317 A162318 A162319 * A162321 A162322 A162323 KEYWORD base,nonn,tabl AUTHOR Leroy Quet, Jul 01 2009 STATUS approved

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Last modified May 29 18:27 EDT 2023. Contains 363042 sequences. (Running on oeis4.)