A157845 a(0) = 1, a(n) = sum of binary digits of all prior terms, expressed in binary.

1, 1, 10, 11, 101, 111, 1010, 1100, 1110, 10001, 10011, 10110, 11001, 11100, 11111, 100100, 100110, 101001, 101100, 101111, 110100, 110111, 111100, 1000000, 1000001, 1000011, 1000110, 1001001, 1001100, 1001111, 1010100, 1010111, 1011100, 1100000, 1100010

Offset

0,3

Comments

Equals A230297 = A010062 converted from decimal to binary, prefixed by another initial 1. - M. F. Hasler, Nov 18 2019

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = A230297(n-1) = A007088(A010062(n-1)) = A007088(A092391(A028897(a(n-1)))) for n > 0. - M. F. Hasler, Nov 18 2019

Maple

b:= proc(n) option remember; `if`(n<2, 1, b(n-1)+
      add(i, i=convert(a(n-1), base, 10)))
    end:
a:= n-> convert(b(n), binary):
seq(a(n), n=0..44);  # Alois P. Heinz, Nov 18 2019

Mathematica

s[0] = s[1] = 1; s[n_] := s[n] = s[n-1] + DigitCount[s[n-1], 2, 1]; Table[FromDigits[IntegerDigits[s[n], 2]], {n, 0, 50}] (* Amiram Eldar, Jul 28 2023 *)

Prog

(PARI) lista(nn) = {my(s = 1); my(t = 1); print1(t, ", "); for (i=1, nn, sb = binary(s); t = subst(Pol(sb), x, 10); print1(t, ", "); s += hammingweight(sb); ); }
(PARI) apply( A157845(n)=fromdigits(binary(A010062(n-!!n))), [0..40]) \\ M. F. Hasler, Nov 18 2019

Crossrefs

Cf. A004207 (base-10 analog); A007088 (n in binary), A010062 (this written in base 10), A000120 (Hammingweight), A092391 (A000120(n) + n), A028897 (convert binary to decimal).

Sequence in context: A037090 A171676 A118240 * A230297 A086084 A206073

Adjacent sequences: A157842 A157843 A157844 * A157846 A157847 A157848

Keyword

base,easy,nonn

Author

Oliver K. Seet, Mar 07 2009

Extensions

a(11) corrected and extended by R. J. Mathar, Mar 12 2009

More terms from Michel Marcus, Apr 19 2014

Status

approved