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A075789
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Value of i, when n is written as r^i - s^j with the smallest possible r^i (with minimal i) and r, s > 0, i, j > 1; or 0 if n is not of this form.
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0
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2, 3, 2, 3, 2, 0, 3, 2, 2, 3, 3, 2, 2, 0, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 5, 2, 2, 5, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 3, 2, 2, 7, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 5, 2, 3, 2, 0, 7, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 7, 0, 7, 2, 2
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OFFSET
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1,1
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COMMENTS
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The zeros are only conjectures (cf. A074981).
"minimal i" means that, if r^i = a^b with composite b, then i is the smallest prime factor of b; e.g., r^i = 3^4 = 9^2, i.e., r = 9, i = 2.
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LINKS
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EXAMPLE
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1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
a(10) = 3 because 10 = 13^3 - 3^7.
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PROG
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(PARI) a(n, LIM=999*n)=for(k=1, LIM, (ispower(k)||k==1)&&ispower(n+k)&&return(factor(ispower(n+k))[1, 1])) \\ M. F. Hasler, May 29 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited and data double-checked with given PARI code by M. F. Hasler, May 29 2018
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STATUS
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approved
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