A123112 Smallest number k such that k^n is equal to the sum of n consecutive primes, or 1 if it does not exist.

2, 6, 11, 12, 3, 18, 81, 90, 81, 942, 1773, 2532, 77, 1866, 637, 126, 1725, 56, 2695, 128, 3647, 6960, 1295, 7180, 10809, 430, 10233, 2944, 3269, 160, 10919, 9068, 40925, 22066, 10763, 558, 1403, 4344, 2943, 8894, 9813, 9308, 4691, 20516, 13801, 8056, 36425

Offset

1,1

Comments

Corresponding numbers m such that a(n)^n = Sum[Prime[i],{i,m,m+n-1}] are {1,7,85,689,13,...} (A162160).

Links

Table of n, a(n) for n=1..47.

Maple

isnp := proc(x, n) local xbar, p, psum, i ; xbar := floor(x/n) ; p := array(1..n) ; p[1] := nextprime(xbar) ; for i from 2 to n do p[i] := nextprime(p[i-1]) ; od ; psum := add(p[i], i=1..n) ; while psum >= x do if psum = x then RETURN(true) ; elif p[1] = 2 then RETURN(false) ; else psum := psum-p[n] ; for i from n to 2 by -1 do p[i] := p[i-1] ; od ; p[1] := prevprime(p[1]) ; psum := psum+p[1] ; fi ; od ; RETURN(false) ; end; A123112 := proc(n) local k ; k := 1 ; while true do if isnp(k^n, n) then RETURN(k) ; else k := k+1 ; fi ; od ; end; for n from 1 to 30 do print(A123112(n)) ; od ; # R. J. Mathar, Jan 13 2007

Prog

(PARI) print1(2); for(n=2, 10, k=n%2; until(s==t, k+=2; t=k^n; s=0; q=t\n; p=q+1; for(i=0, n-1, if(s*n<i*t, q=nextprime(q+1); s+=q, p=precprime(p-1); s+=p))); print1(", "k)) \\ Jens Kruse Andersen, Jul 23 2014

Crossrefs

Cf. A162160.

Sequence in context: A033710 A243157 A274689 * A092189 A228061 A357776

Adjacent sequences: A123109 A123110 A123111 * A123113 A123114 A123115

Keyword

hard,nonn

Author

Alexander Adamchuk, Sep 28 2006

Extensions

More terms from R. J. Mathar, Jan 13 2007

a(17)-a(26) from Max Alekseyev

a(27)-a(43) from Donovan Johnson, Nov 17 2008

a(44)-a(47) from Jens Kruse Andersen, Jul 23 2014

Status

approved