A248366 Least positive integer m such that prime(m+n) - prime(m) divides m + n.

1, 1, 5, 10, 175, 22, 23, 34, 35, 102, 57, 54, 63, 70, 345, 74, 279, 198, 225, 124, 127, 294, 145, 130, 149, 334, 831, 164, 191, 720, 183, 520, 209, 486, 259, 990, 231, 226, 227, 268, 663, 294, 701, 326, 301, 308, 335, 310, 311, 790

Offset: 1

Author

Zhi-Wei Sun, Oct 05 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 except for n = 5, 10, 15, 27.

See also A248369 for a similar conjecture.

Examples

			a(5) = 175 since prime(175+5) - prime(175) = 1069 - 1039 = 30 divides 175 + 5 = 180.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A247824, A248369.

Programs

Mathematica

q[n_]:=q[n]=PartitionsQ[n]
Do[m=1;Label[aa];If[Mod[m+n,Prime[m+n]-Prime[m]]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,50}]

PARI

a(n)=m=1;while((m+n)%(prime(m+n)-prime(m)),m++);m
vector(100,n,a(n)) \\ Derek Orr, Oct 05 2014