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Search: id:A054906
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| A054906 |
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Smallest number x such that Sigma[x+2n]=Sigma[x]+2n (first definition). |
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+0
5
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| 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 7, 5, 3, 3, 7, 5, 3, 5, 3, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 7, 5, 3, 5, 3, 3, 7, 5, 3, 5, 3, 7, 5, 3, 13, 7, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 19, 13, 11, 13, 7, 5, 3, 5, 3, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 7, 5, 3, 7, 5, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 5, 3, 3, 13
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OFFSET
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1,1
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COMMENT
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Least (prime) solutions for Phi[x+2n]=Phi[x]+2n seems to be identical to this sequence, while prime solutions are indeed identical to this sequence.
2nd definition = smallest number x such that Phi[x+2n]=Phi[x]+2n. 3rd definition = smallest primes p such that p+2n=q prime (A020483). The 3 definitions are or conjectured to be identical.
The definitions are not identical if we do not take the smallest numbers. These smallest solutions are believed to be always prime numbers.
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REFERENCES
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Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions. Marcel Dekker,Inc., New York.
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FORMULA
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p=a(n) is the least prime so that p+2n is also a prime (2nd definition).
Minimal solutions to A000203[x+2n]=A000203[x]+2n or to A000010[x+2n]=A000010[x]+2n or to p+2n=q; p, q primes, a(n)=p.
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EXAMPLE
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n-th primes 2,3,5,7,11,13, are solutions to sigma[x+2n]=2n+sigma[x] at 2n=2,6,22,116,88.
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CROSSREFS
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Cf. A023200-A023203, A015913-A015917, A000203, A000010, A020483.
Sequence in context: A003569 A066670 A013606 this_sequence A020483 A138479 A136019
Adjacent sequences: A054903 A054904 A054905 this_sequence A054907 A054908 A054909
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 23 2000
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