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Search: id:A116127
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| A116127 |
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Number of numbers that are congruent to {2, 4} mod 6 between prime(n) and prime(n+1) inclusive. |
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+0
2
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| 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 2, 2, 2, 2, 2, 0, 4, 0, 2, 0, 4, 4, 2, 0, 2, 2, 0, 4, 2, 2, 2, 0, 2, 2, 0, 4, 4, 2, 0, 2, 4, 2, 4, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 0, 4, 0, 2, 2, 2, 2, 2, 0, 2, 4, 2, 2, 2, 2, 2, 4, 0, 6, 2, 4, 2, 2, 0, 2
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Observations up to prime(500000) show that, for n > 2,
A001223(n) = 2 iff a(n) = 0,
A001223(n) = 4 or 6 or 8 iff a(n) = 2,
A001223(n) = 10 or 12 or 14 iff a(n) = 4,
A001223(n) = 16 or 18 or 20 iff a(n) = 6,
................
A001223(n) = 82 or 84 or 86 iff a(n) = 28.
This can be generalized to
A001223(n) = 3*k-2 or 3*k or 3*k+2 iff a(n) = k for k >= 2. A proof should not be too hard.
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PROGRAM
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(MAGMA) [ #[ k: k in [NthPrime(n)..NthPrime(n+1)] | r eq 2 or r eq 4 where r is k mod 6 ]: n in [1..105] ]; /* Klaus Brockhaus, Apr 15 2007 */
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CROSSREFS
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Cf. A000040 (primes), A001223 (differences between consecutive primes), A047235 (numbers congruent to {2, 4} mod 6).
Adjacent sequences: A116124 A116125 A116126 this_sequence A116128 A116129 A116130
Sequence in context: A096030 A025815 A029225 this_sequence A039979 A103668 A076472
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KEYWORD
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nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Apr 08 2007
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EXTENSIONS
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Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 15 2007
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