A250089 5-smooth numbers (A051037) written in base 60, concatenating the decimal values of the sexagesimal digits.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 100, 104, 112, 115, 120, 121, 130, 136, 140, 148, 200, 205, 208, 215, 224, 230, 240, 242, 300, 312, 320, 336, 345, 400, 403, 410, 416, 430, 448, 500, 520, 524, 600

Offset

1,2

Comments

Each pair of digits constitutes the decimal value of a single sexagesimal digit, as on a digital clock, eliminating the colon (:). Any leading zeros are truncated. Thus decimal 64 appears as "104" and not "0104".

References

D. E. Knuth, Ancient Babylonian Algorithms, Communications of the ACM 15 (1972): 671-677.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10540 (Hamming numbers <= 60^10)

Example

a(28) = 112 since A051037(28) = 72. 72 = 1 * 60 + 12, thus sexagesimal 1,12. Concatenating the decimal values of the sexagesimal places gives "112".

Mathematica

a250089[n_Integer] := FromDigits /@ Map[StringJoin, If[# < 10, StringJoin["0", ToString[#]], ToString[#]] & /@ IntegerDigits[#, 60] & /@ Select[Range[n], Last@Map[First, FactorInteger@#] < 7 &], 2]; a250089[360] (* Michael De Vlieger, Nov 11 2014, after Robert G. Wilson v at A051037 *)
With[{n = 360}, Map[FromDigits@ IntegerDigits[#, MixedRadix[ Flatten@ ConstantArray[{6, 10}, {2 Ceiling@ Log[60, n]}]]] &, Union@ Flatten@ Table[2^p1*3^p2*5^p3, {p1, 0, Log[2, n/(1)]}, {p2, 0, Log[3, n/(2^p1)]}, {p3, 0, Log[5, n/(2^p1*3^p2)]}]]] (* Version 10.2, or *)
With[{n = 360}, FromDigits@ StringJoin@ Map[If[# < 10, StringJoin["0", ToString@ #], ToString@ #] &, IntegerDigits[#, 60]] & /@ Union@ Flatten@ Table[2^p1*3^p2*5^p3, {p1, 0, Log[2, n/(1)]}, {p2, 0, Log[3, n/(2^p1)]}, {p3, 0, Log[5, n/(2^p1*3^p2)]}]] (* Michael De Vlieger, Feb 20 2017 *)

Crossrefs

Cf. A051037, A250073, A254334, A254335, A254336.

Sequence in context: A014866 A051661 A051037 * A257997 A070023 A035303

Adjacent sequences: A250086 A250087 A250088 * A250090 A250091 A250092

Keyword

nonn,base

Author

Michael De Vlieger, Nov 11 2014

Status

approved