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

Author

Michael De Vlieger, Nov 11 2014

Keywords

• nonn
• base

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".

Examples

			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".
		

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)

Crossrefs

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

Programs

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 *)