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

Author

Michael De Vlieger, Jan 28 2015

Keywords

• nonn
• base

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".

Examples

			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.
		

Links

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

Crossrefs

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

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

Programs

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 *)

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

Formula

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