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%I M0595 #49 Dec 26 2021 14:15:04
%S 0,1,2,3,4,10,11,12,13,14,20,21,22,23,24,30,31,32,33,34,40,41,42,43,
%T 44,100,101,102,103,104,110,111,112,113,114,120,121,122,123,124,130,
%U 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
%N Numbers in base 5.
%C From _Rick L. Shepherd_, Jun 25 2009: (Start)
%C Nonnegative integers with no decimal digit > 4.
%C Thus nonnegative integers in base 10 whose doubling by normal addition or multiplication requires no carry operation. (End)
%C 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
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Nathaniel Johnston, <a href="/A007091/b007091.txt">Table of n, a(n) for n = 0..10000</a>
%H R. G. Wilson, V, <a href="/A007088/a007088.pdf">Letter to N. J. A. Sloane, Sep. 1992</a>
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F 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
%F a(n) = n + 1/2*Sum_{k >= 1} 10^k*floor(n/5^k). Cf. A037454, A037462 and A102491. - _Peter Bala_, Dec 01 2016
%p 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
%t Table[ FromDigits[ IntegerDigits[n, 5]], {n, 0, 60}]
%o (PARI) a(n)=if(n<1,0,if(n%5,a(n-1)+1,10*a(n/5)))
%o (PARI) apply( A007091(n)=fromdigits(digits(n,5)), [0..66]) \\ _M. F. Hasler_, Nov 18 2019
%o (Python)
%o from gmpy2 import digits
%o def A007091(n): return int(digits(n,5)) # _Chai Wah Wu_, Dec 26 2021
%Y 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).
%Y Cf. A037454, A037462, A102491.
%K nonn,easy,base
%O 0,3
%A _N. J. A. Sloane_, _Robert G. Wilson v_
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