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A159698
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Minimal increasing sequence beginning with 4 such that n and a(n) are either both prime or both composite.
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5
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4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 32, 33, 37, 38, 39, 40, 42, 44, 47, 48, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 67, 68, 71, 72, 74, 75, 79, 80, 81, 82, 84, 85, 89, 90, 91, 92, 93, 94, 97, 98, 101, 102, 104, 105, 106, 108, 109, 110, 111, 112
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OFFSET
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1,1
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COMMENTS
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For n>=11, a(n)=A159559(n-1), which means the two sequences merge.
We may define other sequences a(p-1,n), p prime, which start a(p-1,1)=p-1 and with the same property of n and a(p-1,n) being jointly prime or composite.
We find that for p=7, 11 and 13, the sequences a(6,n), a(10,n) and a(12,n) also merge with the current sequence for sufficiently large n. Does this also hold for primes >=17?
It was verified for primes p with 7<=p<=223 that this sequence a(4,n) and a(p-1,n) eventually merge. The corresponding values of n are 47, 683, 1117, 6257, 390703. - Alois P. Heinz, Mar 09 2011
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..1000
V. Shevelev Several results on sequences which are similar to the positive integers
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FORMULA
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a(1) = 4; for n>1, a(n) = min { m > a(n-1) : m is prime iff n is prime }.
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MAPLE
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a:= proc(n) option remember; local m;
if n=1 then 4
else for m from a(n-1)+1 while isprime(m) xor isprime(n)
do od; m
fi
end:
seq (a(n), n=1..80); # Alois P. Heinz, Nov 21 2010
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CROSSREFS
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Cf. A159559, A159560, A159615, A159619, A159629.
Sequence in context: A032722 A098416 A005556 * A191276 A047377 A188265
Adjacent sequences: A159695 A159696 A159697 * A159699 A159700 A159701
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Shevelev, Apr 20 2009, May 04 2009
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EXTENSIONS
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More terms from Alois P. Heinz, Nov 21 2010
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STATUS
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approved
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