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A176951 Let p = prime(n). Then a(n) = Fibonacci(p+1)/p if this is an integer, otherwise a(n) = Fibonacci(p-1)/p if this is an integer, and fall back to a(n)=0 if both are non-integer.

%I A176951 #29 Jun 09 2025 18:56:25
%S A176951 1,1,0,3,5,29,152,136,2016,10959,26840,1056437,2495955,16311831,
%T A176951 102287808,1627690024,10021808981,25377192720,1085424779823,
%U A176951 2681584376185,17876295136009,113220181313816,1933742696582736
%N A176951 Let p = prime(n). Then a(n) = Fibonacci(p+1)/p if this is an integer, otherwise a(n) = Fibonacci(p-1)/p if this is an integer, and fall back to a(n)=0 if both are non-integer.
%C A176951 This differs only trivially from the better-defined A092330. - _John Blythe Dobson_, Sep 20 2014
%H A176951 Harvey P. Dale, <a href="/A176951/b176951.txt">Table of n, a(n) for n = 1..647</a>
%p A176951 A176951aux := proc(n)
%p A176951         if n = 0 then
%p A176951                 0;
%p A176951         elif combinat[fibonacci](n+1) mod n = 0 then
%p A176951                 combinat[fibonacci](n+1)/n ;
%p A176951         elif combinat[fibonacci](n-1) mod n = 0 then
%p A176951                 combinat[fibonacci](n-1)/n ;
%p A176951         else
%p A176951                 0 ;
%p A176951         end if;
%p A176951 end proc:
%p A176951 A176951 := proc(n)
%p A176951         A176951aux(ithprime(n)) ;
%p A176951 end proc:
%p A176951 seq(A176951(n),n=1..20) ; # _R. J. Mathar_, Oct 29 2011
%t A176951 f[n_] = If[n == 0, 0, If[Mod[Fibonacci[n + 1], n] == 0, Fibonacci[n + 1]/n, If[Mod[Fibonacci[n - 1], n] == 0, Fibonacci[n - 1]/n, 0]]];
%t A176951 Table[f[Prime[n + 1]], {n, 0, 50}]
%t A176951 Table[With[{f1=Fibonacci[p+1],f2=Fibonacci[p-1]},Which[IntegerQ[f1/p],f1/p,IntegerQ[f2/p],f2/p,True,0]],{p,Prime[Range[30]]}] (* _Harvey P. Dale_, Jun 09 2025 *)
%o A176951 (PARI) a(n)=my(p=prime(n),t);t=fibonacci(p+1);if(t%p==0,t/p,t=fibonacci(p-1);if(t%p==0,t/p,0)) \\ _Charles R Greathouse IV_, Oct 29 2011
%Y A176951 Cf. A092330.
%K A176951 nonn
%O A176951 1,4
%A A176951 _Roger L. Bagula_, Apr 29 2010