A100634 a(n) is the decimal equivalent of the binary number whose k-th least significant bit is 1 iff k is a prime number and k <= n.

0, 2, 6, 6, 22, 22, 86, 86, 86, 86, 1110, 1110, 5206, 5206, 5206, 5206, 70742, 70742, 332886, 332886, 332886, 332886, 4527190, 4527190, 4527190, 4527190, 4527190, 4527190, 272962646, 272962646, 1346704470, 1346704470, 1346704470, 1346704470, 1346704470

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 02 2004

Keywords

• nonn
• base

Comments

1 is not considered prime. If 1 were to be considered prime, each term would be incremented by 1.

Examples

			a(5) = 22 because the k-th least significant bits 1,2,3,4,5 are prime for 2,3,5 and not prime for 1,4. So k=1->0, k=2->1, k=3->1, k=4->0 and k=5->1 gives the bit sequence 10110, which is 2 + 4 + 16 = 22 in its decimal expansion.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..300
• Eric Weisstein's World of Mathematics, Least Significant Bit

Crossrefs

Cf. A000040, A080355, A080339, A072762.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 0,
      a(n-1)+`if`(isprime(n), 2^(n-1), 0))
    end:
seq(a(n), n=1..35);  # Alois P. Heinz, Apr 01 2024

Mathematica

Table[FromDigits[Reverse[Table[If[PrimeQ[k] == True, 1, 0], {k, 1, N}]], 2], {N, 1, 40}]
FoldList[Plus, If[PrimeQ[#], 2^#/2, 0] & /@ Range@40] (* David Dewan, Apr 01 2024 *)

PARI

Sum(an)={ L=#binary(an)-1; k=2; s=0; pow2=2;
forstep(j=L, 2, -1,
if(isprime(k), s+=pow2);
k++; pow2*=2);
return(s) };
  n=1; an=0;
while(an<=1346704470,
  an+=Sum(an); print1(an,", "); n++;
  while(!isprime(n), print1(an,", "); n++);
  an=2^(n-1)
) \\ Washington Bomfim, Jan 17 2011