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A110419 Least number k such that (prime(n)-1)! concatenated with k == 0 (mod prime(n)). 2

%I #11 Dec 27 2019 18:52:00

%S 0,1,0,3,12,22,15,24,31,13,38,26,18,14,53,47,41,39,33,29,27,21,17,11,

%T 127,192,176,144,128,209,111,214,178,166,106,245,215,185,165,135,105,

%U 276,236,228,212,204,156,108,319,313,301,283,277,247,229,211,193,187

%N Least number k such that (prime(n)-1)! concatenated with k == 0 (mod prime(n)).

%e a(5) = 12, 10! concatenated with 12 = 362880012 == 0 (mod prime(5)).

%p 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

%t 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 *)

%t 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 *)

%Y Cf. A110418, A110420.

%K base,easy,nonn

%O 1,4

%A _Amarnath Murthy_, Aug 01 2005

%E More terms from _Ryan Propper_ and _Emeric Deutsch_, Aug 05 2005

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)