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5-smooth numbers (A051037) written in base 60, concatenating the decimal values of the sexagesimal digits.
2

%I #15 Feb 20 2017 23:16:17

%S 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,

%T 100,104,112,115,120,121,130,136,140,148,200,205,208,215,224,230,240,

%U 242,300,312,320,336,345,400,403,410,416,430,448,500,520,524,600

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

%C 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".

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

%H Michael De Vlieger, <a href="/A250089/b250089.txt">Table of n, a(n) for n = 1..10540</a> (Hamming numbers <= 60^10)

%e 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".

%t 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 *)

%t 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 *)

%t 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 *)

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

%K nonn,base

%O 1,2

%A _Michael De Vlieger_, Nov 11 2014