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Indices of Ulam prime triples, where u(k), u(k+1) and u(k+2) are all primes, and u(k) = A002858(k) are the Ulam numbers.
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%I #11 May 13 2024 05:21:58

%S 858,1547,2515,3059,9503,9781,11899,11900,13622,15413,18928,22829,

%T 25462,32020,33021,33963,36598,37811,37854,40046,44447,49104,55249,

%U 56526,60847,61741,80658,84414,86235,87971,92832,96674,97185,100004,102684,108025,108273

%N Indices of Ulam prime triples, where u(k), u(k+1) and u(k+2) are all primes, and u(k) = A002858(k) are the Ulam numbers.

%H Amiram Eldar, <a href="/A307330/b307330.txt">Table of n, a(n) for n = 1..1000</a>

%t ulams = {1, 2}; Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[ DeleteCases[Intersection[ulams, n - ulams], n/2, 1, 1]] != 2]; n], {1000}]; p = PrimeQ[ulams]; len = Length[p]; s={}; Do[If[p[[n]]&&p[[n+1]]&&p[[n+2]], AppendTo[s,n]], {n,1,len-2}]; s (* after _Jean-François Alcover_ at A002858 *)

%Y Cf. A002858, A068820, A307328, A307329.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 02 2019