A138342 - OEIS

%I #22 Dec 15 2020 09:07:44

%S 1,9,1,89,1,9,1,889,1,9,1,89,1,9,1,8889,1,9,1,89,1,9,1,889,1,9,1,89,1,

%T 9,1,88889,1,9,1,89,1,9,1,889,1,9,1,89,1,9,1,8889,1,9,1,89,1,9,1,889,

%U 1,9,1,89,1,9,1,888889,1,9,1,89,1,9,1,889,1,9,1,89,1,9,1,8889,1,9,1,89,1,9

%N First differences of A007088.

%H Antti Karttunen, <a href="/A138342/b138342.txt">Table of n, a(n) for n = 1..16383</a>

%F a(n) = A059482(A007814(n)).

%F From _Antti Karttunen_, Nov 06 2018: (Start)

%F a(n) = A007088(n) - A007088(n-1).

%F Multiplicative with a(2^e) = A059482(e), a(p^e) = 1 for odd primes p.

%F (End)

%F G.f.: Sum_{k>=0} 10^k * x^(2^k) / (1 + x^(2^k)). - _Ilya Gutkovskiy_, Dec 14 2020

%e 1-0 = 1, 10-1 = 9, 11-10 = 1, 100-11 = 89, ...

%t Differences[Table[FromDigits[IntegerDigits[n,2]],{n,0,90}]] (* _Harvey P. Dale_, Feb 26 2012 *)

%o (PARI)

%o A007088(n) = fromdigits(binary(n), 10); \\ From A007088.

%o A138342(n) = (A007088(n) - A007088(n-1)); \\ _Antti Karttunen_, Nov 06 2018

%o (PARI)

%o A059482(n) = ((10^n)*(1000/1125) + (1/9));

%o A138342(n) = { my(f=factor(n)); prod(i=1,#f~,if(2==f[i,1],A059482(f[i,2]),1)); }; \\ _Antti Karttunen_, Nov 06 2018

%Y Cf. A007088, A007814, A059482.

%K nonn,mult

%O 1,2

%A Jaume Simon Gispert (jaume(AT)nuem.com), May 17 2008

%E Offset corrected and keyword:mult added by _Antti Karttunen_, Nov 06 2018