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A229791
Integers generated by (a^k+b^k)/(a+b) for all possible positive integer values of a,b,k with b>a.
2
1, 3, 5, 7, 10, 11, 12, 13, 15, 17, 19, 20, 21, 25, 26, 27, 28, 29, 30, 31, 34, 35, 37, 39, 40, 41, 43, 45, 48, 49, 50, 51, 52, 53, 55, 57, 58, 60, 61, 63, 65, 67, 68, 70, 73, 74, 75, 76, 78, 79, 80, 82, 84, 85, 87, 89, 90, 91, 93, 95, 97, 100, 101, 102, 103
OFFSET
1,2
COMMENTS
This form, (a^k+b^k)/(a+b), is a generalization of the Fermat numbers.
Not all integers are in this set.
See A227979 for the complement of this sequence.
LINKS
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
limit=105; lst = {}; Do[p = (a^k + b^k)/(a + b); If[p <= limit && IntegerQ[p], AppendTo[lst, p]], {k, Log[2, 3*limit+1]}, {b, 2, limit*2}, {a, b-1}]; Union[lst]
CROSSREFS
A few of the sequences using this form that identify primes are A000978, A007658, A057469, A128066, A057171, A082387, A122853, A128335.
Sequence in context: A133452 A356665 A251364 * A189293 A140607 A352487
KEYWORD
nonn
AUTHOR
Robert Price, Sep 29 2013
STATUS
approved