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Search: id:A114535
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| A114535 |
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Numbers n that can be represented as (m+1)^k-m^k at least in 3 ways, with k,m>0. |
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1
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OFFSET
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1,2
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COMMENT
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The decompositions for 1 are infinite and trivial, obtained letting k=1 and m arbitrary. The representations for the other entries are: 127 = 64^2-63^2 = 7^3-6^3 = 2^7-1^7, 3367 = 1684^2-1683^2 = 34^3-33^3 = 4^6-3^6, 14911 = 7456^2-7455^2 = 71^3-70^3 = 16^4-15^4. Apparently there are no other solutions for n<10^9.
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EXAMPLE
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127 = 64^2-63^2 = 7^3-6^3 = 2^7-1^7.
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CROSSREFS
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Cf. A115783.
Sequence in context: A024005 A008398 A144969 this_sequence A137789 A005464 A140477
Adjacent sequences: A114532 A114533 A114534 this_sequence A114536 A114537 A114538
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KEYWORD
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hard,more,nonn
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 15 2006
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