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A263537
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Integers k such that A098531(k) is divisible by A000071(k+2).
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1
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1, 2, 13, 25, 31, 43, 55, 61, 73, 85, 91, 103, 115, 121, 133, 145, 151, 163, 175, 181, 193, 205, 211, 223, 235, 241, 253, 265, 271, 283, 295, 301, 313, 325, 331, 343, 355, 361, 373, 385, 391, 403, 415, 421, 433, 445, 451, 463, 475, 481, 493, 505, 511, 523, 535, 541, 553
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OFFSET
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1,2
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COMMENTS
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Sequence is interesting because of the values of a(n) - a(n-1) that are 12 or 6 for n > 3.
a(2) = 2 is the only even term.
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LINKS
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FORMULA
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a(n) = a(n-1)+a(n-3)-a(n-4) for n>6.
G.f.: x*(x^5+5*x^4+11*x^3+11*x^2+x+1) / ((x-1)^2*(x^2+x+1)).
(End)
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EXAMPLE
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a(1) = 1 because 1^5 mod 1 = 0.
a(2) = 2 because (1^5 + 1^5) mod (1 + 1) = 0.
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MATHEMATICA
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PROG
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(PARI) for(n=1, 1e3, if(sum(k=1, n, fibonacci(k)^5) % sum(k=1, n, fibonacci(k)) == 0, print1(n", ")));
(PARI) Vec(x*(x^5+5*x^4+11*x^3+11*x^2+x+1)/((x-1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Oct 20 2015
(Magma) I:=[1, 2, 13, 25, 31, 43]; [n le 6 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..60]]; // Vincenzo Librandi, Nov 20 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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