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

1,2

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007088, A007814, A059482.

Sequence in context: A347490 A038291 A075504 * A101678 A051380 A136238

Adjacent sequences: A138339 A138340 A138341 * A138343 A138344 A138345

Keyword

nonn,mult

Author

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

Extensions

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

Status

approved