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A205372 Least s(k) such that n divides s(k)-s(j) for some j where s=A024675.

%I A205372 #11 Sep 10 2020 03:02:16
%S A205372 6,6,9,12,9,12,18,12,15,26,15,18,30,18,21,34,21,30,34,26,30,26,50,30,
%T A205372 34,30,39,34,50,34,76,50,39,60,39,42,76,42,45,86,45,60,64,50,60,50,56,
%U A205372 60,64,56,60,56,129,60,64,60,69,64,93,64,76,134,69,76,69,72,76
%N A205372 Least s(k) such that n divides s(k)-s(j) for some j<k, where s=A024675.
%C A205372 For a guide to related sequences, see A204892.
%C A205372 a(n) >= n+4, with equality if and only if n+4 is in A024675.
%H A205372 Robert Israel, <a href="/A205372/b205372.txt">Table of n, a(n) for n = 1..10000</a>
%p A205372 N:= 200: # for terms before the first > the greatest prime <= N
%p A205372 P:= select(isprime, [seq(i,i=3..N,2)]):
%p A205372 S:= (P[1..-2]+P[2..-1])/2:
%p A205372 f:= proc(n) local T,R,i;
%p A205372    T:= S mod n;
%p A205372    R:= {}:
%p A205372    for i from 1 to nops(T)-1 do
%p A205372      R:= R union {T[i]};
%p A205372      if member(T[i+1],R) then return S[i+1] fi;
%p A205372    od;
%p A205372    FAIL
%p A205372 end proc:
%p A205372 Res:= NULL:
%p A205372 for n from 1 do
%p A205372   v:= f(n);
%p A205372   if v = FAIL then break fi;
%p A205372   Res:= Res, v
%p A205372 od:
%p A205372 Res; # _Robert Israel_, Sep 09 2020
%t A205372 (See the program at A205153.)
%Y A205372 Cf. A024675, A205153, A204892.
%K A205372 nonn
%O A205372 1,1
%A A205372 _Clark Kimberling_, Jan 26 2012