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A100634
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a(n) = decimal equivalent of binary number whose k-th least significant bit is 1 iff k is a prime number and k <= n.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 1 is not considered prime. If 1 were to be considered prime, each term would be incremented by 1.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..300
Eric Weisstein's World of Mathematics, "Least Significant Bit."
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EXAMPLE
| 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.
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MAPLE
| Table[FromDigits[Reverse[Table[If[PrimeQ[k] == True, 1, 0], {k, 1, N}]], 2], {N, 1, 40}]
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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^(n-1)
) - W. Bomfim webonfim(AT)bol.com Jan 17, 2011
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CROSSREFS
| Cf. A000040, A080355, A080339.
Cf. A072762
Sequence in context: A081518 A135616 A119551 * A130865 A105725 A005226
Adjacent sequences: A100631 A100632 A100633 * A100635 A100636 A100637
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KEYWORD
| nonn,base
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AUTHOR
| Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 02 2004
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