A118123 -id:A118123 - cp's OEIS frontend

A117877 Least p=prime(k) for which A118123(k)=n.

2, 5, 11, 17, 67, 101, 109, 107, 227, 569, 499, 821, 1163, 2153, 1489, 1487, 1579, 4111, 6841, 10739, 5783, 21383, 4729, 3467, 34183, 58741, 19319, 22283, 22279, 22277, 16069, 16067, 17333, 91583, 20479, 20477, 82223, 158363, 31189, 70877, 45061

Offset: 0

Rémi Eismann and Robert G. Wilson v, May 14 2006

nonn

			a(0)=2 because no k exists and it is the least of the three {2, 3 & 7} in A117563 or A117078.
a(1)=5 because 5 + 5 (mod 3) = 7,
a(2)=11 because 11 + 11 (mod 3) = 11 + 11 (mod 9) = 13.
a(3)=17 because 17 + 17 (mod 3) = 17 + 17 (mod 5) = 17 + 17 (mod 15) = 19,
a(4)=67 because 67 + 67 (mod 7) = 67 + 67 (mod 9) = 67 + 67 (mod 21) = 67 + 67 (mod 63) = 71,
a(5)=101 because 101 + 101 (mod 3) = 101 + 101 (mod 9) = 101 + 101 (mod 11) = 101 + 101 (mod 33) = 101 + 101 (mod 99), etc.

Cf. A118123, A117078, A117563.

f[n_] := Block[{p = Prime@n, np = Prime[n + 1]}, Length@ Select[ Divisors[2p - np], # >= np - p &]]; t = Table[0, {50}]; Do[ a = f@n; If[a < 50 && t[[a + 1]] == 0, t[[a + 1]] = n; Print[{a, n, Prime@n}]], {n, 100000}]

A117877(n)={ for( k=n+1, 1e9, n==A118123(k) & return(prime(k)))}

Edited by M. F. Hasler, Nov 07 2009

A118144 Numbers of prime factors of l, where l is defined in A118534.

Original entry on oeis.org

0, 0, 1, 0, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 1, 2, 2, 3, 2, 1, 3, 2, 4, 2, 3, 3, 3, 3, 3, 2, 3, 4, 2, 3, 2, 1, 2, 2, 1, 2, 3, 4, 4, 3, 2, 1, 2, 4, 4, 1, 2

Offset: 1

Rémi Eismann and Fabien Sibenaler, May 14 2006, Feb 14 2008

nonn

a(n) = 0 only for n = 1, 2 and 4.

			For a(1), l=0 thus a(1)=0,
for a(3), l=3 thus a(3)=1,
for a(8), l=15=3*5 thus a(8)=2,
for a(24), l=81=3*3*3*3 thus a(24)=4.

Remi Eismann, Table of n, a(n) for n = 1..10000

Cf. A118534, A117563, A118123, A117078.

a(n) = numbers of factors of l, largest l such that prime(n+1) = prime(n) + (prime(n) mod l), or 0 if no such l exists.

A106752 Numbers of prime factors of k, k defined in A117078.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Rémi Eismann, Jun 22 2007, Feb 14 2008

nonn

a(n) = 0 only for n = 1, 2 and 4.

			For a(1), k=0 thus a(1)=0,
For a(3), k=3 thus a(3)=1,
For a(11), k=25=5*5 thus a(11)=2.

Remi Eismann, Table of n, a(n) for n = 1..10000

Cf. A117078, A117563, A118534, A118144, A118123.

a(n) = numbers of factors of A117078(n). A117078(n) : smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.

cp's OEIS Frontend

A117877 Least p=prime(k) for which A118123(k)=n.

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A118144 Numbers of prime factors of l, where l is defined in A118534.

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A106752 Numbers of prime factors of k, k defined in A117078.

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