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A091067
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Numbers whose odd part is of the form 4k+3.
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32
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3, 6, 7, 11, 12, 14, 15, 19, 22, 23, 24, 27, 28, 30, 31, 35, 38, 39, 43, 44, 46, 47, 48, 51, 54, 55, 56, 59, 60, 62, 63, 67, 70, 71, 75, 76, 78, 79, 83, 86, 87, 88, 91, 92, 94, 95, 96, 99, 102, 103, 107, 108, 110, 111, 112, 115, 118, 119, 120, 123, 124, 126, 127, 131
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OFFSET
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1,1
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COMMENTS
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Either of form 2*a(m) or 4k+3, k >= 0, 0 < m < n.
Numbers n such that Kronecker(-n, m) = Kronecker(m, n) for all m. - Michael Somos, Sep 22 2005
Gives all n for which A005811(n) - A005811(n-1) = -1, from which follows that a(n) = the least k such that A255070(k) = n.
Gives the positions of even terms in A003602.
(End)
Conjecture: alternate definition of same sequence is that a(1)=3 and a(n) is the smallest number > a(n-1) so that no number that is the sum of at most 2 terms in this sequence is a power of 2. - J. Lowell, Jan 20 2024
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LINKS
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FORMULA
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Other identities. For all n >= 1 it holds that:
(End)
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PROG
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(PARI) for(n=1, 200, if(((n/2^valuation(n, 2)-1)/2)%2, print1(n", ")))
(PARI) {a(n) = local(m, c); if( n<1, 0, c=0; m=1; while( c<n, m++; if( ((m/2^valuation(m, 2) - 1) / 2) % 2, c++)); m)}; /* Michael Somos, Sep 22 2005 */
(PARI) a(n) = my(t=1); n<<=1; forstep(i=logint(n, 2), 0, -1, if(bittest(n, i)==t, n++; t=!t)); n; \\ Kevin Ryde, Mar 21 2021
(Haskell)
import Data.List (elemIndices)
a091067 n = a091067_list !! (n-1)
a091067_list = map (+ 1) $ elemIndices 1 a014707_list
(Scheme, with Antti Karttunen's IntSeq-library, two versions)
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CROSSREFS
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First differences are in A106836 (from its second term onward).
Sequence A246590 gives the even terms.
Gives the positions of records (after zero) for A255070 (equally, the position of the first n there).
Cf. A106837 (gives n such that both n and n+1 are terms of this sequence).
Cf. A098502 (gives n such that both n and n+2 are, but n+1 is not in this sequence).
Cf. also A000265, A003602, A004767, A005811, A014707, A034947, A055975, A236840, A255068, A255327, A255330.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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