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%I #12 Jul 14 2021 01:35:39
%S 1,3,4,11,15,19,20,23,24,32,39,48,51,60,67,68,71,75,83,84,88,95,100,
%T 104,111,119,120,127,132,135,143,147,168,180,183,191,195,200,203,204,
%U 207,211,212,219,236,240,243,251,252,255,275,276,284
%N Numbers k such that the sum of the k-th triangular number and the k-th prime is prime.
%H Charles R Greathouse IV, <a href="/A114951/b114951.txt">Table of n, a(n) for n = 1..10000</a>
%e The 11th triangular number is 66, the 11th prime is 31.
%e Their sum is 97, a prime. Therefore 11 is in the sequence.
%t Select[Range[500], PrimeQ[ #*(# + 1)/2 + Prime[ # ]] &]
%o (PARI) list(lim)=my(v=List(),n); forprime(p=2,, if(n++>lim, break); if(isprime(n*(n+1)/2+p), listput(v,n))); Vec(v) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A000217.
%K nonn,less
%O 1,2
%A _J. M. Bergot_, Jun 23 2007
%E Edited and extended by _Stefan Steinerberger_ and _Robert G. Wilson v_, Jun 24 2007
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