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

Author

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

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A118123, A117078, A117563.

Programs

Mathematica

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}]

PARI

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

Extensions

Edited by M. F. Hasler, Nov 07 2009