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A108156 Numbers n such that a(n) is prime, where a(n) = a(n-1) + a(n-2), a(1) = 3794765361567513, a(2) = 20615674205555510.

%I A108156 #33 Feb 16 2025 08:32:58
%S A108156 138,163,190,523,1855,3228,3579,6468,7170,10230,12783,17259,60139,
%T A108156 91315,97923,101823,156075
%N A108156 Numbers n such that a(n) is prime, where a(n) = a(n-1) + a(n-2), a(1) = 3794765361567513, a(2) = 20615674205555510.
%C A108156 In his biography of Paul Erdős, Hoffman cited Wilf's Fibonacci-like primefree sequence (A083216). But, as Weisstein points out, Hoffman inadvertently switched the two initial terms, resulting in a sequence that appears primefree for the first 137 terms. Term 138 is 439351292910452432574786963588089477522344721, which is prime. The first Mathematica program below comes from Weisstein's Mathematica notebook.
%D A108156 Paul Hoffman. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, 1998.
%H A108156 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimefreeSequence.html">Primefree Sequence</a>.
%H A108156 Herbert S. Wilf, <a href="http://www.jstor.org/stable/2690956">Letters to the Editor</a> Math. Mag. 63, 284, 1990.
%t A108156 a[1] := 3794765361567513; a[2] := 20615674205555510; a[n_] := a[n] = a[n - 2] + a[n - 1]; Flatten[Position[Table[a[n], {n, 10^4}], _?PrimeQ]] (* _Eric W. Weisstein_ *)
%t A108156 Flatten[Position[LinearRecurrence[{1,1},{3794765361567513,20615674205555510},160000],_?PrimeQ]] (* _Harvey P. Dale_, Nov 29 2011 *)
%Y A108156 Cf. A083216.
%K A108156 nonn
%O A108156 1,1
%A A108156 _Alonso del Arte_, Jun 06 2005
%E A108156 a(10)-a(12) from _Robert G. Wilson v_, Jun 07 2005
%E A108156 a(13) from _Eric W. Weisstein_, Sep 23 2005
%E A108156 a(14) from _Eric W. Weisstein_, Oct 06 2005
%E A108156 a(15)-a(16) from _Eric W. Weisstein_, Oct 10 2005
%E A108156 a(17) from _Eric W. Weisstein_, Nov 09 2005
%E A108156 Definition adapted to offset by _Georg Fischer_, Jun 18 2021