A118256 Concatenation for i=1 to n of A005171(i); also A118255 in base 2.

1, 10, 100, 1001, 10010, 100101, 1001010, 10010101, 100101011, 1001010111, 10010101110, 100101011101, 1001010111010, 10010101110101, 100101011101011, 1001010111010111, 10010101110101110, 100101011101011101, 1001010111010111010, 10010101110101110101, 100101011101011101011

Offset: 1

Author

Pierre CAMI, Apr 19 2006

Keywords

• nonn
• base
• easy

Examples

			A005171 : 1,0,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,1 ................
a(1)=1, a(2)=10, a(3)=100, a(4)=1001, ...
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000 (terms 1..30 from N. J. A. Sloane)

Crossrefs

Cf. A005171, A118255, A118257.

Programs

Mathematica

Array[FromDigits@ Array[Boole[! PrimeQ@ #] &, #] &, 21] (* or *)
FromDigits@ IntegerDigits[#, 2] & /@ Last@ Transpose@ NestList[{#1 + 1, If[PrimeQ[#1 + 1], 2 #2, 2 #2 + 1]} & @@ # &, {1, 1}, 21] (* Michael De Vlieger, Nov 01 2016, latter after Harvey P. Dale at A118255 *)

PARI

a(n) = sum(k=1, n, !isprime(k)*10^(n-k)); \\ Michel Marcus, Nov 01 2016

Python

from sympy import isprime
def a(n): return int("".join(str(1-isprime(i)) for i in range(1, n+1)))
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Jan 10 2022

Python

# faster version for initial segment of sequence
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    an = 0
    for k in count(1):
        an = 10 * an + int(not isprime(k))
        yield an
print(list(islice(agen(), 21))) # Michael S. Branicky, Jan 10 2022

Formula

a(n) ~ 10^n * 0.10010101.... [Charles R Greathouse IV, Dec 27 2011]

Extensions

Corrected by Omar E. Pol, Nov 08 2007