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Search: id:A116700
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| A116700 |
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"Early bird" numbers: write the natural numbers in a string 12345678910111213.... Sequence gives numbers which occur in the string ahead of their natural place (cf. A117804). |
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+0
15
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| 12, 21, 23, 31, 32, 34, 41, 42, 43, 45, 51, 52, 53, 54, 56, 61, 62, 63, 64, 65, 67, 71, 72, 73, 74, 75, 76, 78, 81, 82, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 110, 111, 112, 121, 122, 123, 131, 132, 141, 142, 151, 152, 161, 162, 171
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Based on an idea by Argentinian puzzle creator Jaime Poniachik, these numbers were introduced by Martin Gardner in 2005 in the magazine Math. Horizons, published by the MAA.
A048992 is a similar sequence, but is different because it does not contain 21, etc. - see comments in A048992.
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REFERENCES
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Martin Gardner, Transcendentals and early birds, Math. Horizons, XIII(2) (2005), pp. 5, 34 (published by Math. Assoc. America).
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LINKS
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Joshua Zucker, Table of n, a(n) for n = 1..675
S. W. Golomb, Early Bird Numbers, Puzzle Column in IEEE Inform. Soc. Newsletter, 52(4) (2002), p. 10.
S. W. Golomb, Early Bird Numbers: Solutions, IEEE Inform. Soc. Newsletter, 53(1) (2003), p. 30.
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FORMULA
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Asymptotically, the early bird numbers have density 1 [Golomb].
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EXAMPLE
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"12" appears at the start of the string, ahead of its position after "11", so is a member.
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PROGRAM
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(ARIBAS) s:= ""; for n:=1 to 200 do sn:=itoa(n);
if substr_index(s, sn) >= 0 then write(n, ", "); end;
s:=concat(s, sn); end; (* Klaus Brockhaus, Jul 23 2007 *)
Ubasic program from Warut Roonguthai (warut822(AT)gmail.com), Jul 23 2007:
10 X=""
20 for N=1 to 396
30 A=cutspc(str(N))
40 if instr(X, A)>0 then print N;
50 X+=A
60 next N
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CROSSREFS
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Cf. A117804. A131881 gives complement.
Cf. A048991 and A048992 (Rollman numbers).
Sequence in context: A129939 A082799 A089320 this_sequence A132132 A085926 A071263
Adjacent sequences: A116697 A116698 A116699 this_sequence A116701 A116702 A116703
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KEYWORD
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nonn,base,nice
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AUTHOR
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Bernardo Recaman Santos (ignotus(AT)hotmail.com), Jul 22 2007
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EXTENSIONS
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More terms from Warut Roonguthai (warut822(AT)gmail.com) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 23 2007.
Golomb links from Jeremy Gardiner, Jul 23 2007
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