A088250
a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.
Original entry on oeis.org
1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
Offset: 1
a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
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a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)
A088651
a(n) = smallest number k such that rk-1 is prime for all r = 1 to n.
Original entry on oeis.org
3, 3, 4, 6, 6, 154770, 2894220, 2894220, 407874180, 214580145780, 9448481062020, 247236503934420, 2545206711847800, 18178612369988250180, 53792264108455702830
Offset: 1
a(5)=6 because 1*6-1, 2*6-1, 3*6-1, 4*6-1, 5*6-1 are all prime.
a(11)=9448481062020 because all eleven numbers 1*9448481062020-1, 2*9448481062020-1,3*9448481062020-1,...,10*9448481062020-1 & 11*9448481062020-1 are prime and 9448481062020 is the smallest number with such property.
A125839
a(n) is the smallest number m such that k*m - 1 is prime for all k=3,4,...,n.
Original entry on oeis.org
1, 1, 6, 18, 120, 1260, 1485540, 28667100, 28667100, 842889105240, 2281585556250, 163881570370980, 45187548280664790
Offset: 3
Luke Pebody (luke.pebody(AT)gmail.com), Jan 02 2007
a(11)=28667100 because 3*28667100-1, 4*28667100-1, 5*28667100-1, 6*28667100-1, 7*28667100-1, 8*28667100-1, 9*28667100-1, 10*28667100-1 & 11*28667100-1 are prime and 28667100 is the smallest number with this property.
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a[n_] := Block[{k = If[n<5, 1, 6], s}, s = k; While[! AllTrue[k Range[3, n] - 1, PrimeQ], k += s]; k]; a /@ Range[3, 9] (* Giovanni Resta, Mar 29 2017 *)
A164325
a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0
Original entry on oeis.org
1, 2, 2, 6, 1170, 64590, 25153800, 25153800, 4747505070, 207187349040, 6703860240000, 26997529639080, 1760354281625940, 1760354281625940, 10718654377787155800
Offset: 1
a(5) corrected by Zak Seidov, Sep 16 2009
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