A006938 Convert the last term from decimal to binary! a(1)=3.

3, 11, 1011, 1111110011, 1000010001110100011000101111011

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base

Comments

The next term (a(6)) has 100 digits. - Harvey P. Dale, Feb 28 2012

The number of digits of a(n) are 1, 2, 4, 10, 31, 100, 330, 1093, 3628, 12049, 40023, 132951, 441651, 1467130, 4873698, 16190071, 53782249, 178660761, ... - Robert G. Wilson v, Jul 10 2013

log(a(n))/log(a(n-1)) ~ log_2(10) = A020862. - Robert G. Wilson v, Jul 10 2013

References

• C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

For initial terms 2 through 12 see A008559, A006938, A260025, A260024, A260026, A260027, A260028, A260029, A008559 (again), A006938 (again), A260030 respectively.

Programs

Mathematica

NestList[FromDigits[IntegerDigits[#,2]]&,3,4] (* Harvey P. Dale, Feb 28 2012 *)

PARI

lista(nn) = my(k=3); print1(k); for(n=2, nn, print1(", ", k=fromdigits(binary(k)))); \\ Jinyuan Wang, Jan 18 2025

Python

def agen(an):
  while True: yield an; an = int(bin(an)[2:])
g = agen(3)
print([next(g) for i in range(5)]) # Michael S. Branicky, Mar 11 2021

Extensions

a(1)=3 added by N. J. A. Sloane, Jul 14 2015