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A123317
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Smallest prime power m such that n+m is a prime number.
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2
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1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 8, 5, 4, 3, 2, 1, 2, 1, 16, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 32, 5, 4, 3, 2, 1, 8, 5, 4, 3, 2, 1, 2, 1, 256, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 16, 5, 4, 3, 2, 1, 4, 3, 2, 1, 128, 5, 4, 3, 2, 1, 8, 7, 16, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..102.
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FORMULA
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A123318(n) = n + a(n);
a(A006093(n)) = 1; a(A040976(n)) = 2 for n>2.
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EXAMPLE
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n=23: 23+1=3*2^3, 23+2=5^2, 23+3=13*2, 23+2^2=3^3, 23+5=7*2^2, 23+7=5*3*2, but 23+8=31=A000040(11), therefore a(23)=8;
n=24: 24+1=5^2, 24+2=13*2, 24+3=3^3, 24+2^2=7*2^2, but 24+5=29=A000040(10), therefore a(24)=5;
the smallest occurring proper odd prime power is 9=3^2:
n=118: 118+1=17*7, 118+2=5*3*2^3, 118+3=11^2, 118+2^2=61*2, 118+5=41*3, 118+7=5^3, 118+2^3=7*2*3^2, but 118+3^2=127=A000040(31), therefore a(118)=9.
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MAPLE
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A123317 := proc(n)
local m ;
m :=1 ;
if isprime(n+m) then
return m ;
end if;
for m from 2 do
if nops(numtheory[factorset](m)) = 1 then
if isprime(n+m) then
return m;
end if;
end if;
end do:
end proc:
seq(A123317(n), n=1..102) ; # R. J. Mathar, Aug 09 2019
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CROSSREFS
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Cf. A013632, A000961.
Sequence in context: A352933 A276976 A135545 * A231557 A171453 A285707
Adjacent sequences: A123314 A123315 A123316 * A123318 A123319 A123320
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Sep 27 2006
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STATUS
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approved
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