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Search: id:A057564
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| A057564 |
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Natural numbers n for which the following three properties hold: (i) Phi[Sigma[n]]=2*Phi[n], (ii) Sigma[n-2]=2*Sigma[Phi[n-2]], (iii) Sigma[n+2]=2*Sigma[Phi[n+2]]. |
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2
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| 666, 19674, 309114, 369594, 715194, 1180026, 1924794, 2722266, 2741274, 4261914, 5564826, 6296634, 6623226, 6826266, 7206906, 9726648, 15956154, 16046874, 16478874, 19263546, 25333146, 27706554, 28151514, 32938074
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Called "Beastly neighbors" because 666 is the least element of the sequence and because these numbers are seen to have a symmetric relationship with their two "neighbors," using analogy to numbering houses on the same side of the street (e.g. 664 and 668 are "neighbors" of 666).
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REFERENCES
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D. Iannucci, "The neighbors of the Beast," Journal of Recreational Mathematics, Volume 31, Number 1, 2002, pp. 52-55.
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EXAMPLE
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Phi[Sigma[666]]=Phi[1482]=432=2*216=2*Phi[666], Sigma[664]=1260=2*630=2*Sigma[328]=Sigma[Phi[664]], Sigma[668]=1176=2*588=2*Sigma[332]=Sigma[Phi[668]]. Thus 666 is an element of the sequence.
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CROSSREFS
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Sequence in context: A043515 A051003 A104181 this_sequence A046694 A138563 A092797
Adjacent sequences: A057561 A057562 A057563 this_sequence A057565 A057566 A057567
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KEYWORD
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easy,nonn
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AUTHOR
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Douglas E. Iannucci (diannuc(AT)uvi.edu), Oct 04 2000
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