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A102730
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Number of factorials contained in n! in binary representation.
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13
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1, 2, 3, 4, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 8, 6, 7, 6, 7, 6, 7, 7, 7, 8, 7, 7, 7, 6, 8, 7, 7, 7, 7, 7, 8, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 8, 8, 7, 7, 7, 8, 8, 7, 8, 7, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Conjecture: the sequence is bounded.
I conjecture the contrary: for every n, there exists k with a(k) > n. [Charles R Greathouse IV, Aug 21 2011]
For n>0: A103670(n) = smallest m such that a(m)=n;
A103671(n) = smallest m such that in binary representation n! doesn't contain m!;
A103672(n) = greatest m less than n such that in binary representation n! contains m!.
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LINKS
| Index entries for sequences related to factorial numbers.
Index entries for sequences related to binary expansion of n
Charles R Greathouse IV, Table of n, a(n) for n = 0..1000
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EXAMPLE
| n=6: 6!=720->'1011010000' contains a(6)=5 factorials: 0!=1->'1', 1!=1->'1', 2!=2->'10', 3!=6->'110' and 6! itself, but not 4!=24->'11000' and 5!=120->'1111000'.
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PROG
| (PARI) contains(v, u)=for(i=0, #v-#u, for(j=1, #u, if(v[i+j]!=u[j], next(2))); return(1)); 0
a(n)=my(v=binary(n--!)); sum(i=0, n-1, contains(v, binary(i!)))+1 \\ Charles R Greathouse IV, Aug 21 2011
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CROSSREFS
| Cf. A036603, A007088, A000142, A011371, A093684, A103673, A103676, A103677, A103674, A103678, A103679, A103675, A103680, A103681.
Sequence in context: A094700 A073635 A071532 * A165597 A099033 A002330
Adjacent sequences: A102727 A102728 A102729 * A102731 A102732 A102733
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 07 2005
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