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Search: id:A124689
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| A124689 |
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Position of the first n in the decimal expansion of e^n, or -1 if the digits of n never appear. |
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+0
1
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| -1, 3, 17, 7, 2, 8, 19, 23, 3, 8, 53, 71, 290, 5, 157, 36, 201, 52, 48, 41, 214, 14, 38, 131, 48, 17, 19, 21, 33, 8, 50, 19, 315, 282, 3, 355, 43, 9, 135, 11, 19, 65, 114, 85, 123, 108, 312, 263, 59, 11, 148, 0, 168, 296, 26, 25, 55, 4, 82, 23, 96, 147, 141, 39, 596, 50, 7, 36, 373, 97, 9, 6, 129, 85, 52, 153, 3, 111, 47, 153, 309, 217
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Conjecture: -1 only occurs in the first entry of the sequence. 1000 digits precision was used in the calculation.
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FORMULA
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e = 2.718281828...
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EXAMPLE
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e^0 = 1, 0 does not occur so -1 is in first entry in the table.
e^1 = 2.718281828..., first 1 occurs in the third position so 3 is the second entry.
e^2 = 7.3890560989306502272304274..., first 2 occurs in the 17th position, so 17 is the third entry in the table.
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PROGRAM
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(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) }
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CROSSREFS
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Sequence in context: A109216 A090478 A140446 this_sequence A093844 A033467 A096475
Adjacent sequences: A124686 A124687 A124688 this_sequence A124690 A124691 A124692
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KEYWORD
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base,easy,sign
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Dec 25 2006
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