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

1,2

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

Links

Table of n, a(n) for n=1..18.

Formula

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

Example

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.

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

Prog

(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], " ")))

Crossrefs

Cf. A001597, A002808, A053767, A141092.

Sequence in context: A229743 A151520 A282517 * A002270 A286358 A088228

Adjacent sequences: A227246 A227247 A227248 * A227250 A227251 A227252

Keyword

nonn,more

Author

Robin Garcia, Jul 04 2013

Extensions

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

Status

approved