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A062619
Numbers k such that 53^k - 52^k is a prime.
0
3, 19, 29, 37, 1879, 3181, 3331, 19597, 38993, 84239, 90679
OFFSET
1,1
COMMENTS
Terms greater than 1000 often correspond only to strong pseudoprimes. [Clarified by M. F. Hasler, Sep 15 2013]
All terms are prime. - Robert Price, Jan 20 2013
a(12) > 10^5. - Robert Price, Jan 20 2013
To elaborate on Robert Price's comment that all terms are prime: This is also true for all other sequences of numbers n such that k^n - (k-1)^n is prime. It is easy to prove by elementary means that if n = a * b, then k^n - (k-1)^n is divisible by k^(n-a) - (k-1)^(n-a) and k^(n-b) - (k-1)^(n-b). - Alonso del Arte, Sep 15 2013
KEYWORD
nonn,hard
AUTHOR
Mike Oakes, May 18 2001, May 19 2001
EXTENSIONS
a(8)-a(11) from Robert Price, Jan 20 2013
STATUS
approved