A073860 Smallest primes such that every partial sum is an n-th power.

2, 7, 503, 1889, 30367

Offset

1,1

Comments

The sequence is complete. Proof: We must find a prime p and an integer x such that p = x^6 - (2+7+503+1889+30367) = x^6 - 32768 = (x^2-32)*(x^4+32*x^2+1024). Since p is prime, we must have p=1*p, therefore we can only have x=sqrt(33) to make p = (1)*(3169). However, sqrt(33) is not an integer. Therefore we can conclude that there is no prime p satisfying the equation. - Francois Jooste (pin(AT)myway.com), Mar 09 2003

Links

Table of n, a(n) for n=1..5.

Formula

a(n) = x^n - Sum_{i=1..n-1} a(i), for some integer x and a(n) prime for all n. - Francois Jooste (pin(AT)myway.com), Mar 09 2003

Example

a(3) = 503, 2+7+503 = 512 = 8^3.

Crossrefs

Sequence in context: A321134 A027732 A073698 * A093926 A065590 A051249

Adjacent sequences: A073857 A073858 A073859 * A073861 A073862 A073863

Keyword

fini,full,nonn

Author

Amarnath Murthy, Aug 15 2002

Status

approved