A154703 Concatenation of the first n primes written in base 2.

10, 1011, 1011101, 1011101111, 10111011111011, 101110111110111101, 10111011111011110110001, 1011101111101111011000110011, 101110111110111101100011001110111, 10111011111011110110001100111011111101, 1011101111101111011000110011101111110111111

Offset: 1

Author

Jonathan Vos Post, Jan 14 2009

Keywords

• base
• easy
• nonn

Comments

Number of bits in a(n) = Sum_{i=1..n} A035100(i). See A328659(n).

Examples

			a(2) = 1011 = 10 Concat 11 = (2 base 2) Concat (3 base 2).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..122

Crossrefs

Cf. A000040, A004676, A007088, A035100, A328659.

Programs

Maple

A154703 := proc(n) option remember: local d: if(n=1)then return 10: fi: d:=convert(ithprime(n),base,2): return parse(cat(convert(procname(n-1),string), convert(op(convert(d,base,10,10^nops(d))),string))): end: seq(A154703(n),n=1..10); # Nathaniel Johnston, May 27 2011
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 0,
      parse(cat(a(n-1), convert(ithprime(n), binary))))
    end:
seq(a(n), n=1..12);  # Alois P. Heinz, Dec 16 2024

Mathematica

With[{p = IntegerDigits[Prime[Range[15]], 2]}, Array[FromDigits[Flatten[p[[;;#]]]] &, Length[p]]] (* Paolo Xausa, Feb 26 2024 *)

PARI

a(n) = fromdigits(concat(apply(binary, primes(n)))); \\ Michel Marcus, Jul 17 2023

Formula

a(n) = CONCATENATE[i=1..n] A004676(i) = CONCATENATE[i=1..n] A007088(A000040(i)).

Extensions

Corrected terms a(6) and beyond from Seiichi Manyama, Jul 17 2023