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%I #13 Jan 14 2021 22:07:40
%S -1,3,17,7,2,8,19,23,3,8,53,71,290,5,157,36,201,52,48,41,214,14,38,
%T 131,48,17,19,121,33,8,50,19,315,282,3,355,43,9,135,11,19,65,114,85,
%U 123,108,312,263,59,11,148,80,168,296,26,25,55,4,82,23,96,147
%N Position of the first n in the decimal expansion of e^n, or -1 if the digits of n never appear.
%C Conjecture: -1 only occurs in the first entry of the sequence. 1000-digit precision was used in the calculation.
%F e = 2.718281828...
%e e^0 = 1, 0 does not occur so -1 is in first entry in the table.
%e e^1 = 2.718281828..., first 1 occurs in the third position so 3 is the second entry.
%e e^2 = 7.3890560989306502272304274..., first 2 occurs in the 17th position, so 17 is the third entry in the table.
%t Join[{-1},Table[SequencePosition[RealDigits[E^n,10,1000][[1]], IntegerDigits[ n],1][[1,1]],{n,90}]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 06 2017 *)
%t {-1}~Join~Table[Position[Partition[#, IntegerLength@ n, 1], IntegerDigits@ n][[1, 1]] &@ First@ RealDigits[E^n, 10, 10^4], {n, 90}] (* _Michael De Vlieger_, Mar 06 2017 *)
%o (PARI) digitposexp(n) = \ Exponential e, expansion first occurrence of n { local(x,y,r,dot); for(x=0,n, r = exp(x); if(r==floor(r), y=find(Str(floor(r)),x), y=find(Str(r),x); dot=find(Str(r),"."); if(dot < y, y--); ); if(y, print1(y","),print1(-1",") ) ) } find(str,match) = \Return the position of the first occurrence of string \match in string str { local(lnm,lns,x,c,i); str=Str(str); \This allows leaving quotes off input match=Str(match); c=0; i=0; lns=length(str); lnm=length(match); if(lnm>1,i=1); x=1; while(x<=lns-lnm+1, if(mid(str,x,lnm)== match,break,x++); ); if(x>lns,return(0),return(x)) } mid(str,s,n) = \ Get a substring of length n from string str starting at position s in str. { local(v,ln,x,tmp); v =""; tmp = Vec(str); ln=length(tmp); for(x=s,s+n-1, v=concat(v,tmp[x]); ); return(v) } iscube(n) = { local(r); r = n^(1/3); if(floor(r+.5)^3== n,1,0) }
%K base,easy,sign
%O 0,2
%A _Cino Hilliard_, Dec 25 2006
%E Corrected by _Harvey P. Dale_, Mar 06 2017
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