A008559 a(1)=2; thereafter, convert a(n-1) from base 10 to base 2 but regard the result as a base 10 number.

2, 10, 1010, 1111110010, 1000010001110100011000101111010

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice

Comments

The previous number is converted to binary digits and then the digits are regarded as decimal digits in the next number in the sequence. - Michael Somos, May 16 2014

The next term has 100 digits. - Harvey P. Dale, Jul 16 2011

The number of decimal digits of a(n) is A242347(n). - 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

• Clifford Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..7

Crossrefs

Cf. A006937 (essentially the same sequence).

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

Programs

Maple

f:=proc(n) local i,j,r; i:=convert(n,base,2); j:=add(i[r]*10^(r-1),r=1..nops(i)); end;
g:=proc(n,M) global f; local a,b,t1; a:=n; t1:=[a]; for i from 1 to M do b:=f(a); t1:=[op(t1),b]; a:=b; od; t1; end; g(2,5); # N. J. A. Sloane, Jul 14 2015

Mathematica

NestList[FromDigits[IntegerDigits[#,2]]&,2,5] (* Harvey P. Dale, Jul 16 2011 *)

PARI

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

Python

A008559_list = [2]
for _ in range(5):
    A008559_list.append(int(bin(A008559_list[-1])[2:]))
# Chai Wah Wu, Dec 26 2014

Extensions

Comment corrected by Chai Wah Wu, Dec 26 2014