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A094787 a(n) = smallest prime p such that p + n is a perfect power m^k, k >= 2. 1
3, 2, 5, 5, 3, 2, 2, 17, 7, 17, 5, 13, 3, 2, 17, 11, 19, 7, 13, 5, 11, 3, 2, 3, 2, 23, 5, 53, 3, 2, 5, 17, 3, 2, 29, 13, 107, 11, 61, 41, 23, 7, 101, 5, 19, 3, 2, 73, 79, 31, 13, 29, 11, 67, 73, 113, 7, 23, 5, 61, 3, 2, 37, 17, 79, 59, 61, 13, 31, 11, 29, 53, 71, 7, 53, 5, 23, 3, 2, 41, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: every prime is contained in this sequence.

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

2+8=10, 3+8=11, 5+8=13, 7+8=15, 11+8=19, 13+8, 17+8=25. 17 is the first prime that when added to 8 gives a perfect power, viz. 25.

MAPLE

A094787 := proc(n)

    local i ;

    for i from 1 do

        if isA001597(ithprime(i)+n) then

            return ithprime(i) ;

        end if;

    end do:

end proc:

seq(A094787(n), n=1..40) ; # R. J. Mathar, Nov 15 2019

PROG

(PARI) k(n, m) = for(j=1, m, forprime(x=2, n, if(ispower(x+j), print1(x", "); break))) ispower(n) = { local(p, r, j); r = sqrt(n); for(j=2, floor(r), p = floor(log(n)/log(j)+.5); if(j^p ==n, return(1)); ); return(0) }

(MAGMA) a:=[]; for n  in [1..81] do p:=2; while not IsPower(p+n) do p:=NextPrime(p); end while; Append(~a, p); end for; a; // Marius A. Burtea, Nov 15 2019

CROSSREFS

Sequence in context: A159587 A124732 A167552 * A132778 A182289 A127738

Adjacent sequences:  A094784 A094785 A094786 * A094788 A094789 A094790

KEYWORD

nonn

AUTHOR

Cino Hilliard, Jun 10 2004

EXTENSIONS

Offset corrected by R. J. Mathar, Nov 15 2019

STATUS

approved

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)