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Search: id:A045572
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| A045572 |
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Numbers that are odd but not divisible by 5. |
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+0
12
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| 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 93, 97, 99, 101, 103, 107, 109, 111, 113, 117, 119, 121, 123, 127, 129, 131, 133, 137, 139, 141, 143, 147, 149, 151, 153
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Contains the repunits R_n, (A000042 or A002275): For any m in the sequence (divisible by neither 2 nor 5), Euler's theorem (i.e. m|10^m-1=9*R_n) guarantees that R_n is always some multiple of m (see A099679) and thus forms a subsequence. - Lekraj Beedassy (blekraj(AT)yahoo.com), Oct 26 2004
Inverse formula: n = 4*floor(a(n)/10) + floor([a(n) mod 10]/3) + 1 - Carl R. White (oeisfan(AT)phodd.net), Feb 06 2008
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FORMULA
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a(n)=-1+Sum_{k=0..n}{(1/12)*{5*(k mod 4)+11*[(k+1) mod 4]-[(k+2) mod 4]+5*[(k+3) mod 4]}} - Paolo P. Lava (ppl(AT)spl.at), Dec 20 2007
a(n) = 10*floor((n-1)/4) + 2*floor( (4*[(n-1) mod 4]+1)/3 ) + 1 a(n) = a(n-1) + 2 + 2*floor([(x+6) mod 10]/9) - Carl R. White (oeisfan(AT)phodd.net), Feb 06 2008
a(n) = 2*n + 2*floor((n-3)/4) + 1 - Kenneth Hammond (weregoose(AT)gmail.com), Mar 07 2008
a(n) = -1 + 2*n + 2*floor((n+1)/4) - Kenneth Hammond (weregoose(AT)gmail.com), Mar 25 2008
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EXAMPLE
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a(18) = 10*floor(17/4) + 2*floor( (4*[17 mod 4]+1)/3 ) + 1
= 10*4 + 2*floor( (4*[1]+1)/3 ) + 1
= 40 + 2*floor(5/3) + 1
= 40 + 2*1 + 1
= 43
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PROGRAM
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/*GNU bc code*/ scale=0; for(n=1; n<=100; n++) 10*((n-1)/4)+2*((4*((n-1)%4)+1)/3)+1 - Carl R. White (oeisfan(AT)phodd.net), Feb 06 2008
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CROSSREFS
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See also A085820.
Sequence in context: A097270 A005818 A085820 this_sequence A134445 A069254 A080903
Adjacent sequences: A045569 A045570 A045571 this_sequence A045573 A045574 A045575
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KEYWORD
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easy,nonn
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AUTHOR
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Jeff Burch (gburch(AT)erols.com)
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