A254334 Powers of 3 in base 60, concatenating the decimal values of the sexagesimal digits.

1, 3, 9, 27, 121, 403, 1209, 3627, 14921, 52803, 162409, 491227, 2273721, 7225203, 22083609, 106254827, 319172521, 957521603, 2953364809, 12940502427, 42902311321, 132707334003, 402122410009, 2010408030027, 6031224090121, 18093712270403, 54285137211209

Offset

0,2

Comments

Each sexagesimal digit appears as a pair of decimal digits as on a digital clock. Any leading zeros are truncated. Thus decimal 81 appears as "121" and not "0121".

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1200

Formula

a(n) = A055643(A000244(n)). - Michel Marcus, Mar 02 2015

Example

a(6) = 1209, since 3^6 = 729 = 12 * 60^1 + 9, thus 12:09 in clock-like notation, which becomes 1209 when restricted to numeric characters.

Mathematica

f[n_] := FromDigits@ StringJoin[If[# < 10, StringJoin["0", ToString[#]], ToString[#]] & /@ IntegerDigits[3^n, 60]]; Table[f@ i, {i, 0, 26}] (* Michael De Vlieger, Jan 28 2015 *)

Prog

(PARI) a(n) = subst(Pol(digits(3^n, 60)), x, 100); \\ Michel Marcus, Feb 22 2015
(Python)
def digits(n, b=10): # list of digits of n in base b
....x, y = n, []
....while x >= b:
........x, r = divmod(x, b)
........y.append(r)
....y.append(x)
....return list(reversed(y))
A254334_list = [int(''.join([format(x, '02d') for x in digits(3**i, 60)])) for i in range(10**2)]
# Chai Wah Wu, Mar 14 2015

Crossrefs

Cf. A000244 (Powers of 3), A055643 (Babylonian numbers).

Cf. Sexagesimal representations: A250073 (Powers of 2), A254335 (Powers of 5), A254336 (Powers of 10).

Sequence in context: A323927 A146151 A306681 * A375093 A028855 A299597

Adjacent sequences: A254331 A254332 A254333 * A254335 A254336 A254337

Keyword

nonn,base

Author

Michael De Vlieger, Jan 28 2015

Status

approved