

A100634


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


2



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
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OFFSET

1,2


COMMENTS

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


LINKS

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


EXAMPLE

a(5)=22 because the kth 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.


MATHEMATICA

Table[FromDigits[Reverse[Table[If[PrimeQ[k] == True, 1, 0], {k, 1, N}]], 2], {N, 1, 40}]


PROG

(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^(n1)
) \\ Washington Bomfim, Jan 17 2011


CROSSREFS

Cf. A000040, A080355, A080339, A072762.
Sequence in context: A258702 A320916 A119551 * A242527 A304680 A325803
Adjacent sequences: A100631 A100632 A100633 * A100635 A100636 A100637


KEYWORD

nonn,base


AUTHOR

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


STATUS

approved



