1,3

Numbers whose digits in base 2 are in nonincreasing order.

Might be called "nialpdromes".

Subset of A077436. Proof: Since a(n) is of form (2^i-1)2^j, i,j>=0, a(n)^2 = [2^(2i)-2^(i+1)]2^(2j) + 2^(2j) where the first sum term has i-1 one bits and its 2j-th bit is zero, while the second sum term switches the 2j-th bit to one, giving i one bits, as in a(n). - Ralf Stephan, Mar 08 2004

Numbers n such that binary representation contains no "01". - Benoit Cloitre (benoit7848c(AT)orange.fr), May 23 2004

Every polynomial with coefficients equal to 1 for the leading terms and 0 after that, evaluated at 2. For instance a(13) = x^4 + x^3 + x^2 at 2, a(14) = x^4 + x^3 + x^2 + x at 2. - Ben Thurston (benthurston27(AT)yahoo.com), Jan 11 2008

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

a(n)=2^s(n) - 2^{[s(n)^2+s(n)-2n]/2} where s(n) = ceiling{[ -1+sqrt(1+8n)]/2} - Sam Alexander (amnalexander(AT)yahoo.com), Jan 08 2005

a(n) = 2^k + a(n-k-1) for 1 < n and k = A003056(n-2). The rows of T(r, c) = 2^r-2^c for 0 <= c < r read from right to left produce this sequence: 1; 2, 3; 4, 6, 7; 8, 12, 14, 15; ... - Frank Ellermann, Dec 06, 2001

For n>0, a(n) mod 2 == A010054(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 23 2004

A140130(a(n))=1 and for n>1: A140129(a(n))=A002262(n-2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2008

a(22) = 64 = 32 + 32 = 2^5 + a(16) = 2^A003056(20) + a(22-5-1).

a(23) = 96 = 64 + 32 = 2^6 + a(16) = 2^A003056(21) + a(23-6-1).

a(24) = 112 = 64 + 48 = 2^6 + a(17) = 2^A003056(22) + a(24-6-1).

a:=proc(n) local n2, d: n2:=convert(n, base, 2): d:={seq(n2[j]-n2[j-1], j=2..nops(n2))}: if n=0 then 0 elif n=1 then 1 elif d={0, 1} or d={0} or d={1} then n else fi end: seq(a(n), n=0..2100); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 22 2006

(PARI) for(n=0, 2500, if(prod(k=1, length(binary(n))-1, component(binary(n), k)+1-component(binary(n), k+1))>0, print1(n, ", ")))

A000337(r) = sum of row T(r,c) with 0 <= c < r. See also A003056.

Sequence in context: A114391 A077436 A082752 this_sequence A054784 A018585 A018399

Adjacent sequences: A023755 A023756 A023757 this_sequence A023759 A023760 A023761

nonn,base,easy

Olivier Gerard (ogerard(AT)ext.jussieu.fr)

Definition changed by njas, Jan 05 2008