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A112591
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Sequence describing the exclusive OR operation on consecutive prime numbers.
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2
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1, 6, 2, 12, 6, 28, 2, 4, 10, 2, 58, 12, 2, 4, 26, 14, 6, 126, 4, 14, 6, 28, 10, 56, 4, 2, 12, 6, 28, 14, 252, 10, 2, 30, 2, 10, 62, 4, 10, 30, 6, 10, 126, 4, 2, 20, 12, 60, 6, 12, 6, 30, 10, 506, 6, 10, 2, 26, 12, 2, 62, 22, 4, 14, 4, 118, 26, 10, 6, 60, 6, 8, 26, 14, 4, 250, 8, 28, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| When represented in binary, this series represents the un-common bits in two consecutive prime numbers. Sudden occurrence of a big number in this series holds special interest.
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FORMULA
| f[n] = p[n]^p[n + 1]; where p[n] is the n-th prime number
f[n] = p[n]^p[n + 1]; where p[n] is the n-th prime number - Christopher M. Herron (cmh285(AT)psu.edu), Apr 25 2006
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EXAMPLE
| f(2) = 6 ; since p[2] = 3, p[3] = 5; and 3^5 = 6
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MAPLE
| A112591 := proc(n) local ndual, n2dual, nxor, i ; ndual := convert(ithprime(n), base, 2) ; n2dual := convert(ithprime(n+1), base, 2) ; nxor := [] ; i := 1 ; while i <= nops(ndual) do nxor := [op(nxor), abs(op(i, ndual)-op(i, n2dual)) ] ; i := i+1 ; od ; while i <= nops(n2dual) do nxor := [op(nxor), op(i, n2dual) ] ; i := i+1 ; od ; add( op(i, nxor)*2^(i-1), i=1..nops(nxor)) ; end: for n from 1 to 80 do printf("%d, ", A112591(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 07 2007
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CROSSREFS
| Sequence in context: A065284 A050088 A163864 * A106034 A194036 A194100
Adjacent sequences: A112588 A112589 A112590 * A112592 A112593 A112594
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KEYWORD
| nonn
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AUTHOR
| Sandeep Chellappen (sandeep.chellappen(AT)gmail.com), Dec 18 2005
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EXTENSIONS
| More terms from Christopher M. Herron (cmh285(AT)psu.edu), Apr 25 2006
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