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A248369
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Least positive integer m such that prime(m+n) - prime(m) divides m.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(7) = 80 since prime(80+7) - prime(80) = 449 - 409 = 40 divides 80.
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MATHEMATICA
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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 *)
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PROG
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(PARI)
a(n)=m=1; while(m%(prime(m+n)-prime(m)), m++); m
vector(100, n, a(n)) \\ Derek Orr, Oct 05 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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