login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; graph; refs; listen; history; text; internal format)
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 A191772

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)