%I #31 Dec 02 2018 02:45:12

%S 1,4,6,21,80,4151,6982,269563,779693,834365,16176645,19770092,

%T 41049539,228612936,1950787140,2404785364,3095996836,5236785750

%N Number of consecutive composites beginning with the first, to be added to obtain a power.

%C All powers are squares with the exception of 3^3 for a(2) and 6^9 for a(6). I conjecture these are the only nonsquare powers.

%C a(19) > 10^10. - _Zak Seidov_, Jul 06 2013

%F {n: A053767(n) in A001597}. - _Zak Seidov_, Jul 06 2013

%e Considering 1 not to be prime and not to be composite, first composite is 4 which is 2^2. And the sum of the first four composites is 4 + 6 + 8 + 9 = 27 = 3^3.

%p # see A001597 for isA001597

%p for n from 1 do

%p if isA001597(A053767(n) ) then

%p print(n) ;

%p end if;

%p end do: # _R. J. Mathar_, Jul 08 2013

%o (PARI) : n=10^7;v=vector(n);i=0;for(a=2,n,if(isprime(a),next,i++;v[i]=a));k=0;for(j=1,i,k=k+v[j];if(ispower(k,,&n),print1([k,n,j]," ")))

%Y Cf. A001597, A002808, A053767, A141092.

%K nonn,more

%O 1,2

%A _Robin Garcia_, Jul 04 2013

%E a(11) - a(18) from _Zak Seidov_, Jul 06 2013