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A007091 Numbers in base 5.
(Formerly M0595)
314
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 (list; graph; refs; listen; history; text; internal format)
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
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).
Sequence in context: A037325 A293292 A037469 * A058185 A080897 A117383
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)