A227249 Number of consecutive composites beginning with the first, to be added to obtain a power.

1, 4, 6, 21, 80, 4151, 6982, 269563, 779693, 834365, 16176645, 19770092, 41049539, 228612936, 1950787140, 2404785364, 3095996836, 5236785750

Offset: 1

Author

Robin Garcia, Jul 04 2013

Keywords

• nonn
• more

Comments

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.

a(19) > 10^10. - Zak Seidov, Jul 06 2013

Examples

			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.
		

Crossrefs

Cf. A001597, A002808, A053767, A141092.

Programs

Maple

# see A001597 for isA001597
for n from 1 do
    if isA001597(A053767(n) ) then
        print(n) ;
    end if;
end do: # R. J. Mathar, Jul 08 2013

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]," ")))

Formula

{n: A053767(n) in A001597}. - Zak Seidov, Jul 06 2013

Extensions

a(11) - a(18) from Zak Seidov, Jul 06 2013