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 A110419 Least number k such that (prime(n)-1)! concatenated with k == 0 (mod prime(n)). 2
 0, 1, 0, 3, 12, 22, 15, 24, 31, 13, 38, 26, 18, 14, 53, 47, 41, 39, 33, 29, 27, 21, 17, 11, 127, 192, 176, 144, 128, 209, 111, 214, 178, 166, 106, 245, 215, 185, 165, 135, 105, 276, 236, 228, 212, 204, 156, 108, 319, 313, 301, 283, 277, 247, 229, 211, 193, 187 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Table of n, a(n) for n=1..58. EXAMPLE a(5) = 12, 10! concatenated with 12 = 362880012 == 0 (mod prime(5)). MAPLE c0:=proc(x, y) local s: s:=proc(m) nops(convert(m, base, 10)) end: if y=0 then 10*x else x*10^s(y)+y: fi end: a:=proc(n) local p: p:=proc(k) if c0((ithprime(n)-1)!, k) mod ithprime(n) = 0 then k else fi end: [seq(p(k), k=0..400)][1] end: seq(a(n), n=1..75); # c0 yields the concatenation of two numbers # Emeric Deutsch, Aug 05 2005 MATHEMATICA Do[p = Prime[n]; k = 0; s = ToString[(p-1)! ]; While[Mod[ToExpression[s <> ToString[k]], p] > 0, k++ ]; Print[k], {n, 1, 50}] (* Ryan Propper, Aug 05 2005 *) lnk[n_]:=Module[{p=Prime[n], c, k=0}, c=(Prime[n]-1)!; While[Mod[ c*10^ IntegerLength[ k]+k, p]!=0, k++]; k]; Join[{0, 1, 0}, Array[lnk, 60, 4]] (* Harvey P. Dale, Dec 27 2019 *) CROSSREFS Cf. A110418, A110420. Sequence in context: A051656 A074004 A088099 * A031223 A063598 A063107 Adjacent sequences: A110416 A110417 A110418 * A110420 A110421 A110422 KEYWORD base,easy,nonn AUTHOR Amarnath Murthy, Aug 01 2005 EXTENSIONS More terms from Ryan Propper and Emeric Deutsch, Aug 05 2005 STATUS approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)