

A227249


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


2



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



