Search: a108116 -id:a108116
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A143789
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Lightest finite monotonically increasing sequence obtained by chunking an 18-digit Skolem-Langford integer (see A108116). There are d digits between two d's in the sequence.
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+20
1
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4, 5, 6, 7, 8, 41, 51, 63, 72, 83, 200
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OFFSET
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1,1
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COMMENTS
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"Lightest" --> the weight of such a sequence is the sum of all its terms; "Finite" --> by definition all such sequences are finite; "Monotonically" --> no two adjacent terms in the sequence are the same; "Increasing" --> a(n) < a(n+1); "Chunking" --> cutting in slices. The original Skolem-Langford number is 456784151637283200 [this is a(14565) in "D. Wilson, Complete table of n, a(n) for n = 1..20120", which can be found at A108116] and this integer, properly chunked, produces the sequence]. In the sequence there is no digit between the two 0's, there is one digit between the two 1's, there are two digits between the two 2's,... there are eight digits between the two 8's. This sequence has been computed by Dan Hoey.
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LINKS
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Table of n, a(n) for n=1..11.
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CROSSREFS
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Cf. A108116 and A132291
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KEYWORD
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base,easy,fini,nonn
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AUTHOR
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Dan Hoey and Eric Angelini, Sep 01 2008
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STATUS
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approved
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A132291
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Base 10 strong Skolem-Langford numbers.
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+10
4
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12132003, 23121300, 30023121, 31213200, 1214230043, 1312432004, 2342131400, 2412134003, 3004312142, 3400324121, 4002342131, 4131243200, 1213267345006475, 1213275364005746, 1214267540036573, 1214273645300765, 1214275640035763, 1215247365430076
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OFFSET
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1,1
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COMMENTS
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Self-describing numbers: between two digits "d" there are d digits.
a(n) has either 0 or 2 instances of any digit, hence even number of digits.
"Strong" means that every digit from 0 to the largest digit of a(n) must be present in a(n).
Number of digits of a(n) == 0 or 2 (mod 8)
Largest element is a(2820) = 867315136875420024.
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LINKS
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D. Wilson, Complete table of n, a(n) for n = 1..2820
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CROSSREFS
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Base 10 Skolem-Langford numbers are in A108116.
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KEYWORD
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base,easy,fini,full,nonn
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AUTHOR
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Eric Angelini, Jun 26 2005, Aug 10 2007
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EXTENSIONS
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Edited by N. J. A. Sloane, Nov 18 2007
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STATUS
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approved
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A307748
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Weak Skolem-Langford numbers that are prime.
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+10
0
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2412134003, 2742300437, 141753400357, 171450034753, 191453004359, 246200431613, 267240036473, 293251310059, 386732002687, 394530041519, 426724001617, 451714350037, 460054236253, 463724326007, 491514300539, 497514100579, 497524121579, 592632513169, 642732463007, 683002362181, 685200265181
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graph;
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text;
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OFFSET
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1,1
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COMMENTS
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Prime terms of A108116.
Largest element is a(411) = 973006384792642181. - Jinyuan Wang, Jul 23 2019
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LINKS
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Table of n, a(n) for n=1..21.
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MATHEMATICA
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Select[Last /@ Cases[ Import[ "https://oeis.org/A108116/b108116.txt", "Table"], {_Integer, _Integer}], PrimeQ] (* based on A108116 b-file, Giovanni Resta, Jul 03 2019 *)
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CROSSREFS
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Cf. A108116, A132291.
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KEYWORD
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base,easy,fini,nonn
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AUTHOR
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Lekraj Beedassy, Apr 26 2019
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STATUS
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approved
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