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Search: id:A091361
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| 1, 2, 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99
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OFFSET
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1,2
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COMMENT
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Apart from 1 and 2 it is conjectured that the only values present are congruent to 3 mod 6 (all these values are present).
Comment from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 25 2008 (Start) Proof of the conjecture that this is 1 and 2 followed by A016945 follows by considering the 6 cases n=6k-1, 6k, 6k+1, 6k+2, 6k+3 or 6k+4, individual evaluation of A001840(n) with their corresponding 3 formulas quoted in A001840 in each case, and searching for solutions of the form A001840(n) = t*n for integer t.
Example: A0001840[6k+4]=A0001840[3(2k+1)+1]=(2k+2)(6k+5)/2=t*(6k+4) implies t=k+7/6+1/[6(3k+2)] which cannot be solved in integers t and k. So numbers of the form 6k+4 are not members here. (End)
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EXAMPLE
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A001840(9)=18, so 9 is in the sequence.
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CROSSREFS
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Cf. A001840.
Sequence in context: A108825 A109663 A056702 this_sequence A092352 A061933 A124881
Adjacent sequences: A091358 A091359 A091360 this_sequence A091362 A091363 A091364
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Mar 01 2004
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