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

1,2

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.

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A247824, A248366.

Sequence in context: A221413 A145003 A386927 * A097645 A153333 A284858

Adjacent sequences: A248366 A248367 A248368 * A248370 A248371 A248372

Keyword

nonn

Author

Zhi-Wei Sun, Oct 05 2014

Status

approved