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 A123317 Smallest prime power m such that n+m is a prime number. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA A123318(n) = n + a(n); a(A006093(n)) = 1; a(A040976(n)) = 2 for n>2. EXAMPLE 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. MAPLE 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 CROSSREFS Cf. A013632, A000961. Sequence in context: A352933 A276976 A135545 * A231557 A171453 A285707 Adjacent sequences: A123314 A123315 A123316 * A123318 A123319 A123320 KEYWORD nonn AUTHOR Reinhard Zumkeller, Sep 27 2006 STATUS approved

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Last modified February 4 14:43 EST 2023. Contains 360055 sequences. (Running on oeis4.)