A138342 First differences of A007088.

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, 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, 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

Offset: 1

Author

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

Keywords

• nonn
• mult

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383

Crossrefs

Cf. A007088, A007814, A059482.

Programs

Mathematica

Differences[Table[FromDigits[IntegerDigits[n,2]],{n,0,90}]] (* Harvey P. Dale, Feb 26 2012 *)

PARI

A007088(n) = fromdigits(binary(n), 10); \\ From A007088.
A138342(n) = (A007088(n) - A007088(n-1)); \\ Antti Karttunen, Nov 06 2018

PARI

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

Formula

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

From Antti Karttunen, Nov 06 2018: (Start)

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

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

(End)

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

Extensions

Offset corrected and keyword:mult added by Antti Karttunen, Nov 06 2018