A248369 Least positive integer m such that prime(m+n) - prime(m) divides m.

1, 6, 54, 18, 26, 24, 80, 120, 180, 48, 70, 160, 92, 82, 220, 98, 228, 102, 378, 130, 348, 152, 158, 172, 202, 372, 204, 720, 206, 448, 218, 560, 236, 228, 222, 1480, 282, 1656, 636, 300, 312, 322, 764, 350, 356, 352, 362, 420, 434, 860

Offset: 1

Author

Zhi-Wei Sun, Oct 05 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0. Moreover, for n > 9 we have a(n) < n^2 except for n = 12, 19, 36, 38.

Note that for each n > 1 the term a(n) should be even and at least 2*n.

Examples

			a(7) = 80 since prime(80+7) - prime(80) = 449 - 409 = 40 divides 80.
		

Links

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

Crossrefs

Cf. A000040, A247824, A248366.

Programs

Mathematica

Do[m=1;Label[aa];If[Mod[m,Prime[m+n]-Prime[m]]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,50}]
lpi[n_]:=Module[{m=1},While[Mod[m,Prime[n+m]-Prime[m]]!=0,m++];m]; Array[ lpi,50] (* Harvey P. Dale, Jan 17 2022 *)

PARI

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