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#20 by N. J. A. Sloane at Fri Jan 10 12:24:23 EST 2020
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#19 by Felix Fröhlich at Mon Dec 09 13:40:22 EST 2019
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#18 by Felix Fröhlich at Mon Dec 09 13:38:05 EST 2019
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| NAME
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a(n) is the smallest number k > 0 such that for each b = 2..n the base-b expansion of k has exactly n - b zeros.
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Discussion
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| Mon Dec 09
| 13:40
| Felix Fröhlich: So, should the second comment be removed?
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#17 by Felix Fröhlich at Mon Dec 09 13:37:33 EST 2019
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| DATA
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31, 2, 10, 18, 271
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| OFFSET
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2,12
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| PROG
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a(n) = for(k=21, oo, for(b=2, n, if(count_zeros(digits(k, b))!=n-b, break, if(b==n, return(k)))))
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| EXTENSIONS
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Value of a(2) adjusted by Felix Fröhlich, Dec 09 2019
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| STATUS
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proposed
editing
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#16 by Stefano Spezia at Mon Dec 09 03:55:21 EST 2019
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Discussion
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| Mon Dec 09
| 04:06
| Michel Marcus: I asked Felix if he could come and see
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| 13:35
| Felix Fröhlich: Regarding the value of a(2): it is 3 because this is the value the program returns for n = 2 :P I do agree that it makes sense to also permit 1.
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#15 by Stefano Spezia at Mon Dec 09 03:53:29 EST 2019
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| KEYWORD
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nonn,base,fini,full,new
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| STATUS
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proposed
editing
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Discussion
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| Mon Dec 09
| 03:55
| Stefano Spezia: For finite sequences totally given in DATA the keyword “full” together with “fini” is necessary
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#14 by Christopher Cormier at Sun Dec 08 14:56:27 EST 2019
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#13 by Christopher Cormier at Sun Dec 08 14:54:17 EST 2019
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| COMMENTS
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This list is complete. Proof: When converting base 2 to base 4, we can group the digits in base 2 into pairs from the least significant bit. We then convert pairs into single digits in base 4 as 00 -> 0, 01 -> 1, 10 -> 2, 11 -> 3. This always causes the number of zeros to go to half or less than half. For all n >= 7, n-4 is greater than (n-2)/2, so the condition is impossible. - Christopher Cormier, Dec 08 2019
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| KEYWORD
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nonn,base,hard,morefini,new
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| STATUS
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approved
editing
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Discussion
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| Sun Dec 08
| 14:56
| Christopher Cormier: Why is the first value in the sequence 3 instead of a(2) = 1? 1 in binary is still 1 which has no zeros.
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#12 by Giovanni Resta at Tue Dec 03 03:44:47 EST 2019
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#11 by Peter Luschny at Tue Dec 03 03:30:46 EST 2019
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