A007091 Numbers in base 5. (Formerly M0595)

0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 200, 201, 202, 203, 204, 210, 211, 212, 213, 214, 220, 221, 222, 223, 224, 230

Offset

0,3

Comments

From Rick L. Shepherd, Jun 25 2009: (Start)

Nonnegative integers with no decimal digit > 4.

Thus nonnegative integers in base 10 whose doubling by normal addition or multiplication requires no carry operation. (End)

It appears that this sequence corresponds to the numbers n for which twice the sum of digits of n is the sum of digits of 2*n. - Rémy Sigrist, Nov 22 2009

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992

Index entries for 10-automatic sequences.

Formula

a(0)=0 a(n)=10*a(n/5) if n==0 (mod 5) a(n)=a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002

a(n) = n + 1/2*Sum_{k >= 1} 10^k*floor(n/5^k). Cf. A037454, A037462 and A102491. - Peter Bala, Dec 01 2016

Maple

A007091 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n, base, 5): return op(convert(l, base, 10, 10^nops(l))): end: seq(A007091(n), n=0..58); # Nathaniel Johnston, May 06 2011

Mathematica

Table[ FromDigits[ IntegerDigits[n, 5]], {n, 0, 60}]

Prog

(PARI) a(n)=if(n<1, 0, if(n%5, a(n-1)+1, 10*a(n/5)))
(PARI) apply( A007091(n)=fromdigits(digits(n, 5)), [0..66]) \\ M. F. Hasler, Nov 18 2019
(Python)
from gmpy2 import digits
def A007091(n): return int(digits(n, 5)) # Chai Wah Wu, Dec 26 2021

Crossrefs

Cf. A000042 (base 1), A007088 (base 2), A007089 (base 3), A007090 (base 4), A007092 (base 6), A007093 (base 7), A007094 (base 8), A007095 (base 9).

Cf. A037454, A037462, A102491.

Sequence in context: A037325 A293292 A037469 * A058185 A080897 A117383

Adjacent sequences: A007088 A007089 A007090 * A007092 A007093 A007094

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Robert G. Wilson v

Status

approved