id:A117563 - OEIS Search Results

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a(n) = A118534(n)/A117078(n) unless A117078(n) = 0 in which case a(n) = 0.

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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; listen)

	OFFSET	`1,5`
	COMMENT	`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.`
	LINKS	`Remi Eismann, Table of n, a(n) for n = 1..10000` `Remi Eismann, Java program to decompose a prime as weightlevel + gap, or A117078(n)A117563(n) + A001223(n)).` `Remi Eismann, Decomposition of natural numbers into weight * level + jump and application to a new classification of prime numbers`
	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`
	CROSSREFS	`Cf. A117078, A118534.` `Adjacent sequences: A117560 A117561 A117562 this_sequence A117564 A117565 A117566` `Sequence in context: A133094 A122510 A102662 this_sequence A060439 A135224 A013597`
	KEYWORD	`nonn`
	AUTHOR	`Remi Eismann (reismann(AT)free.fr), Apr 29 2006, Feb 14 2008`
	EXTENSIONS	`More terms from Robert G. Wilson v, May 05, 2006` `Edited by njas, May 14 2006`

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Last modified May 12 19:26 EDT 2008. Contains 139661 sequences.

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