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 A116345 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8. 6

%I #13 Jul 17 2021 01:44:54

%S 41,54,40354308,59645687,39704957106129738595969799927611,

%T 44505281604832422780051712184760,45053875613995255103944518907120,

%U 54946124386004744896055481092875,55494718395167577219948287815235,60295042893870261404030200072384,68683652917306421895276391964227

%N Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8.

%H Robert Israel, <a href="/A116345/b116345.txt">Table of n, a(n) for n = 1..41</a>

%e 59645687 * 59645693 = 35576083//35576091, where // denotes concatenation.

%p f:= proc(d) local R;

%p R:= map(rhs@op,{msolve(x^2=17,10^d+1)});

%p R:= map(t -> (t-3) mod (10^d+1), R);

%p op(select(proc(t) local m; m:= (t*(t+6)-8)/(10^d+1)+8; m >= 10^(d-1) and m < 10^d end proc, R));

%p end proc;

%p sort(convert({seq(f(i),i=1..50)},list)); # _Robert Israel_, Jan 17 2017

%Y Cf. A116168, A116339, A116344, A116346, A116352.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006

%E More terms from _Robert Israel_, Jan 17 2017

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Last modified June 23 11:44 EDT 2024. Contains 373644 sequences. (Running on oeis4.)