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A059876
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a(n) = bin_prime_sum(n).
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8
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2, 1, 3, 3, 5, 7, 9, -1, 1, 3, 5, 5, 7, 9, 11, 3, 5, 7, 9, 9, 11, 13, 15, 13, 15, 17, 19, 19, 21, 23, 25, -7, -5, -3, -1, -1, 1, 3, 5, 3, 5, 7, 9, 9, 11, 13, 15, 7, 9, 11, 13, 13, 15, 17, 19, 17, 19, 21, 23, 23, 25, 27, 29, -3, -1, 1, 3, 3, 5, 7, 9, 7, 9, 11, 13, 13, 15, 17, 19, 11, 13, 15, 17, 17, 19, 21, 23, 21, 23, 25, 27, 27, 29, 31, 33, 19, 21, 23, 25, 25, 27, 29, 31, 29, 31
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| From R. J. Mathar, Nov 12 2011. (Start)
The function bin_prime_sum of an argument n is a sum of three numbers. Let s = A000523(n) be the exponent of the largest power of 2 less than or equal to n and prime=A000040. Then the three terms are:
i) (-1)^(n+1);
ii) sum_{i=1..s} prime(i) * (1 + (-1)^[n/2^i] ); where [..] is the floor bracket;
iii) 1 (if n=1), otherwise prime(s) (if s even) or 0 (if s odd). (End)
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MAPLE
| with(numtheory); bin_prime_sum := proc(n) local i, s; s := floor_log_2(n); RETURN(((-1)^(n+1)) + add( (((-1)^(floor(n/(2^i))+1))*ithprime(i)), i=1..s) + (`if`((1 = n), 1, ((`mod`((s+1), 2))*ithprime(s)))) ); end;
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CROSSREFS
| Cf. A059871, A059872, A059873, A059877, A059878, A059880. E.g. A059876[A059873[n]] = A000040[n]
Sequence in context: A058689 A173510 A190568 * A095354 A132883 A132888
Adjacent sequences: A059873 A059874 A059875 * A059877 A059878 A059879
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KEYWORD
| sign
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AUTHOR
| Antti Karttunen Feb 05 2001
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