A004654 Powers of 2 written in base 15. (Next term contains a non-decimal character.)

1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 918, 1331, 2662

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base

Comments

a(14) is defined as "2^14 written in base 15". However, the base-15 digits of 2^14 are [4,12,12,4]. The standard convention of using letters A, B, ... to represent digits > 9, cannot be used in the Data sections of OEIS entries. One possibility to encode such terms within the given constraints and without affecting the earlier terms would be to use 00, 10, 20, ..., 50 to represent unambiguously the digits 0, 10, 11, ..., 14. - M. F. Hasler, Jun 22 2018.

This sequence makes a nice puzzle. It would be possible to allow non-decimal characters by using pairs of decimal digits instead of single digits, but this would spoil the beauty of the puzzle. - N. J. A. Sloane, Jun 25 2018

Crossrefs

Cf. A000079, A004643, ..., A004655: powers of 2 written in base 10, 4, 5, ..., 16.

Cf. A000244, A004656, A004658, A004659, ...: powers of 3 in base 10, 2, 4, 5, ...

Programs

PARI

apply( a(n,b=15,m=2)=fromdigits(digits(m^n,b)), [0..13]) \\ This sums the base-15 digits multiplied by powers of 10. Digits > 9 occurring for n >= 14 will carry over to the left (4CC4 -> 5324). - M. F. Hasler, Jun 22 2018