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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.
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]
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.
Cf. A117078, A118534.
Sequence in context: A122510 A102662 A142048 * A060439 A206283 A135224
Adjacent sequences: A117560 A117561 A117562 * A117564 A117565 A117566
Rémi Eismann, Apr 29 2006, Feb 14 2008
More terms from Robert G. Wilson v, May 05 2006
Edited by N. J. A. Sloane, May 14 2006