Revision History for A098951
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#18 by N. J. A. Sloane at Tue Mar 26 20:41:53 EDT 2019
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#17 by Michael B. Porter at Mon Mar 25 02:18:25 EDT 2019
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#16 by Michael B. Porter at Mon Mar 25 02:15:15 EDT 2019
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| EXAMPLE
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After a(30) = 89, a(31) must start with an even digit. A number consisting of one even digit would work, but they are all in the sequence already. A 2-digit number with first digit even and second digit odd would work, but they are also all in the sequence already. A 3-digit number would have to have even, odd, and even digits in that order. The smallest such number is 210, so a(31) = 210. - Michael B. Porter, Mar 25 2019
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reviewed
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#15 by Joerg Arndt at Sun Mar 24 07:53:12 EDT 2019
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Discussion
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| Sun Mar 24
| 08:10
| M. F. Hasler: What else could it mean? If a cycle would be possible, why not 0,1,0,1,....?
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| 08:37
| Michel Marcus: offset 0 or 1 ? but one may wonder why they are not the same ?
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| 14:11
| M. F. Hasler: Yes indeed. Same author, nearly same date, same terms up to a(32)...
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| Mon Mar 25
| 00:23
| M. F. Hasler: This is not a permutation of the nonetheless integers because (in addition to the bad offset ;-)) it has only numbers with digits with alternating parity.
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| 00:24
| M. F. Hasler: *nonnegative (my phone keeps un-correcting what I type :-( !)
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#14 by M. F. Hasler at Sat Mar 23 22:05:54 EDT 2019
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Discussion
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| Sun Mar 24
| 06:13
| Georg Fischer: For me it's not quite obvious whether "available" in the name implies "not yet in the sequence". If not, I would ask for the non-existance of a cycle, if so, then whether it si (not) a permutation of the non-negative numbers?
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#13 by M. F. Hasler at Sat Mar 23 21:53:36 EDT 2019
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| COMMENTS
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Indeed, A097962 is required to be increasing. Therefore, a(31) = 210 can here be followed by a(32) = 10, while A097962(32) = 301. - M. F. Hasler, Mar 23 2019
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| STATUS
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approved
editing
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Discussion
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| Sat Mar 23
| 22:05
| M. F. Hasler: Given the first terms, I think it would have been natural to start at offset 0.
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#12 by Giovanni Resta at Wed Mar 05 13:32:54 EST 2014
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#11 by T. D. Noe at Wed Mar 05 13:29:11 EST 2014
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#10 by T. D. Noe at Wed Mar 05 13:28:55 EST 2014
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| NAME
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Smallest available integer fitting the even/odd/even/odd/even... digit pattern. (across adjacent numbers).
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| DATA
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 210, 10, 12, 14, 16, 18, 30, 32, 34, 36, 38, 50, 52, 54, 56, 58, 70, 72, 74, 76, 78, 90, 92, 94, 96, 98, 101, 212, 103, 214, 105, 216, 107, 218, 109, 230, 121, 232, 123
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| OFFSET
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01,3
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| LINKS
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T. D. Noe, <a href="/A098951/b098951.txt">Table of n, a(n) for n = 1..10000</a>
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#9 by T. D. Noe at Wed Mar 05 13:13:27 EST 2014
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| MATHEMATICA
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(* longer, but faster *) eoQ[n_] := Module[{d = IntegerDigits[n], alt, i}, alt = Table[If[OddQ[i], -1, 1], {i, d}]; i = 1; While[i++; i <= Length[d] && alt[[i]] == alt[[1]]*(-1)^(i + 1)]; If[i <= Length[d], alt[[1]] = 0]; alt[[1]]]; nn = 10000; tev = {}; tod = {}; Do[If[eoQ[i] == -1, AppendTo[tod, i], If[eoQ[i] == 1, AppendTo[tev, i]]], {i, nn}]; t = {0}; While[tev != {} && tod != {}, If[OddQ[t[[-1]]], AppendTo[t, tev[[1]]]; tev = Rest[tev], AppendTo[t, tod[[1]]]; tod = Rest[tod]]]; t (* T. D. Noe, Mar 05 2014 *)
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proposed
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