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A374173
a(n) is the smallest prime whose base-n representation contains a run of at least n identical digits.
0
3, 13, 683, 3907, 55987, 960803, 19173967, 435848051, 11111111113, 1540683021299, 19453310068921, 328114698808283, 45302797058044219, 469172025408063623, 19676527011956855059, 878942778254232811943, 120353718818554114936591, 109912203092239643840221
OFFSET
2,1
COMMENTS
a(2) to a(18) are all increasing, but a(19) is smaller than a(18).
EXAMPLE
a(2) = 3 = 11_2.
a(3) = 13 = 111_3.
a(11) = 1540683021299 = 544444444444_11.
a(18) = 120353718818554114936591 = 3111111111111111111_18.
a(19) = 109912203092239643840221 = 1111111111111111111_19.
MATHEMATICA
d[n_]:=d[n]=Table[Table[m, n], {m, 0, n-1}];
dpre[n_]:=Flatten[Table[{m}~Join~#&/@d[n], {m, 0, n-1}], 1];
dpost[n_]:=Flatten[Table[Map[#~Join~{m}&, d[n]], {m, 0, n-1}], 1];
dprepost[n_]:=Flatten[Table[Map[{j}~Join~#~Join~{m}&, d[n]], {m, 0, n-1}, {j, 0, n-1}], 2];
c[n_]:=c[n]=DeleteDuplicates[Sort[Select[FromDigits[#, n]&/@Join[d[n], dpre[n], dpost[n], dprepost[n]], #>n&]]];
a[n_]:=a[n]=Do[If[PrimeQ[q], Return[q]; Break[]; ], {q, c[n]}];
Table[a[n], {n, 2, 19}]
CROSSREFS
Sequence in context: A222762 A290376 A089711 * A173759 A001039 A357855
KEYWORD
base,nonn
AUTHOR
Robert P. P. McKone, Jun 30 2024
STATUS
approved