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Search: id:A073860
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| A073860 |
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Smallest primes such that every partial sum is an n-th power. |
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+0
3
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OFFSET
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1,1
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COMMENT
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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
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FORMULA
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a(n) = x^n - sum(a(i), i=1..n-1), for some integer x and a(n) prime for all n. - Francois Jooste (pin(AT)myway.com), Mar 09 2003
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EXAMPLE
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a(3) = 503, 2+7+503 = 512=8^3.
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CROSSREFS
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Sequence in context: A110386 A027732 A073698 this_sequence A093926 A095304 A065590
Adjacent sequences: A073857 A073858 A073859 this_sequence A073861 A073862 A073863
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KEYWORD
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fini,full,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 15 2002
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