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0, 0, 1, 0, 3, 1, 5, 3, 1, 9, 1, 3, 13, 3, 1, 1, 19, 5, 9, 23, 1, 15, 11, 9, 3, 33, 11, 35, 21, 3, 3, 5, 45, 3, 49, 5, 1, 3, 23, 1, 59, 9, 63, 27, 65, 11, 1, 3, 75, 45, 1, 79, 21, 35, 1, 1, 89, 5, 39, 93, 21, 9, 3, 103, 3, 3, 25, 3, 115, 69, 1, 39, 19, 1, 75, 29, 3, 3, 3, 21, 139, 3, 143, 61, 87
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| a(n) is the "level" of prime(n).
There is a unique decomposition of the primes: provided the level a(n) is > 0, we have prime(n) = weight * level + gap, or A000040(n)=A117078(n)*a(n)+A001223(n).
a(n) = 0 only for primes 2, 3 and 7.
A118534(n) = prime(n) - g(n) or A000040(n) - A001223(n) if prime(n) - g(n) > g(n), 0 otherwise.
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LINKS
| Remi Eismann, Table of n, a(n) for n = 1..10000
Remi Eismann, Java program to decompose a prime as weight*level + gap, or A117078(n)*A117563(n) + A001223(n)).
Rémi Eismann, Decomposition into weight * level + jump and application to a new classification of primes, arXiv:0711.0865 [math.NT]
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EXAMPLE
| a(7)=15/3=5; a(14)=39/13=3; a(16)=47/47=1; a(18)=55/11=5; a(29)=105/5=11
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CROSSREFS
| Cf. A117078, A118534.
Sequence in context: A122510 A102662 A142048 * A060439 A206283 A135224
Adjacent sequences: A117560 A117561 A117562 * A117564 A117565 A117566
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KEYWORD
| nonn
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AUTHOR
| Remi Eismann (reismann(AT)free.fr), Apr 29 2006, Feb 14 2008
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EXTENSIONS
| More terms from Robert G. Wilson v, May 05, 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 14 2006
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