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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

Table of n, a(n) for n=1..102.

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.)