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Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 3.
6

%I #9 Jul 19 2021 19:54:26

%S 150,186,324,376,666,2046,3000,82650,100384,466716,1322316,4049584,

%T 67820074,110003884,135734074,156502836,196043286,213017754,238849000,

%U 261405396,289940826,310507774,365294050,398891964,446667216

%N Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 3.

%C Also numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 1.

%p cc:=proc(x,y) local s: s:=proc(m) nops(convert(m,base,10)) end: x*10^s(y)+y: end: a:=proc(n) if type(sqrt(9+4*cc(n,n+4)),integer) then n else fi end: seq(a(n),n=1..500000); # very slow; cc yields the concatenation of x and y; - _Emeric Deutsch_, May 05 2007

%Y Cf. A116112, A115428, A115429, A116316, A116199, A116172, A116329.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006

%E Edited by _N. J. A. Sloane_, Apr 14 2007