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Search: id:A063957
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| A063957 |
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Numbers not of the form round[m*sqrt(2)] for any integer m, i.e. complement of A022846. |
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1
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| 2, 5, 9, 12, 15, 19, 22, 26, 29, 32, 36, 39, 43, 46, 50, 53, 56, 60, 63, 67, 70, 73, 77, 80, 84, 87, 90, 94, 97, 101, 104, 108, 111, 114, 118, 121, 125, 128, 131, 135, 138, 142, 145, 149, 152, 155, 159, 162, 166, 169, 172, 176, 179, 183, 186, 189, 193, 196, 200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Similar to Beatty sequences: where a pair of complementary Beatty sequences are floor[n*c] and floor[n*c/(c-1)] for c an irrational constant > 1, these pairs of complementary sequences are in general round[n*c] and round[(n-1/2)*c/(c-1)] for c an irrational constant > 1.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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a(n) =round[(n-1/2)*(2+sqrt(2))] =round[n*3.4142...-1.7071...]
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EXAMPLE
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round[m*sqrt(2)] starts 1,3,4,6,7,8,10,11,13,... so this sequence must start 2,5,9,12,...
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PROGRAM
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(PARI) { f=2 + sqrt(2); t=f/2; for (n=1, 1000, write("b063957.txt", n, " ", round(n*f - t)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 03 2009]
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CROSSREFS
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Cf. A001951, A001952, A007064, A022846. Consider natural numbers A000027 as a triangle 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc., then the a(n) indicate rows without a square.
Sequence in context: A057471 A099434 A108165 this_sequence A047385 A086814 A086343
Adjacent sequences: A063954 A063955 A063956 this_sequence A063958 A063959 A063960
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Sep 04 2001
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