A283984 Sums of distinct nonzero terms of A007489: a(n) = Sum_{k>=0} A030308(n,k)*A007489(1+k).

0, 1, 3, 4, 9, 10, 12, 13, 33, 34, 36, 37, 42, 43, 45, 46, 153, 154, 156, 157, 162, 163, 165, 166, 186, 187, 189, 190, 195, 196, 198, 199, 873, 874, 876, 877, 882, 883, 885, 886, 906, 907, 909, 910, 915, 916, 918, 919, 1026, 1027, 1029, 1030, 1035, 1036, 1038, 1039, 1059, 1060, 1062, 1063, 1068, 1069, 1071, 1072, 5913

Offset: 0

Author

Antti Karttunen, Mar 19 2017

Keywords

• nonn

Comments

Indexing starts from zero, with a(0) = 0.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A000142, A007489, A030308, A059590, A070939, A276075, A276091, A283477, A283985.

Programs

PARI

A007489(n) = sum(k=1, n, k!);
A030308(n,k) = bittest(n,k);
A283984(n) = sum(i=0,(#binary(n)-1),A030308(n,i)*A007489(1+i));

Scheme

(define (A283984 n) (A276075 (A283477 n)))

Formula

a(n) = Sum_{i=0..A070939(n)} A030308(n,i)*A007489(1+i).

a(n) = A276075(A283477(n)).

Other identities. For all n >= 0:

a(2^n) = A007489(n+1).