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A117563 a(n) = A118534(n)/A117078(n) unless A117078(n) = 0 in which case a(n) = 0. 78
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; text; internal format)
OFFSET
1,5
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.
LINKS
Remi Eismann, Java program to decompose a prime as weight*level + gap, or A117078(n)*A117563(n) + A001223(n)).
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.
MATHEMATICA
a34[n_] := If[n == 1 || n == 2 || n == 4, 0, 2 Prime[n] - Prime[n+1]];
a78[n_] := Block[{a, p = Prime[n], np = Prime[n+1]}, a = Min[Select[ Divisors[2p - np], # > np - p& ]]; If[a == Infinity, 0, a]];
a[n_] := If[a78[n] == 0, 0, a34[n]/a78[n]];
Array[a, 85] (* Jean-François Alcover, Nov 02 2018, after Robert G. Wilson v in A118534 *)
CROSSREFS
Sequence in context: A102662 A350279 A142048 * A060439 A206283 A135224
KEYWORD
nonn
AUTHOR
Rémi Eismann, Apr 29 2006, Feb 14 2008
EXTENSIONS
More terms from Robert G. Wilson v, May 05 2006
Edited by N. J. A. Sloane, May 14 2006
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)