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Prime indices of triangular numbers k such that either k + 1 or k - 2 is prime.
1

%I #5 Sep 15 2024 22:04:55

%S 3,5,7,11,13,17,19,23,29,37,41,43,47,53,61,71,73,89,97,107,131,149,

%T 157,163,167,179,193,197,211,223,233,251,257,269,271,277,281,307,313,

%U 337,359,389,401,409,419,431,439,443,457,467,503,509,521,541,571,613,641,673,691

%N Prime indices of triangular numbers k such that either k + 1 or k - 2 is prime.

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 496 at p. 155.

%e 29 is a term since it is prime and A000217(29) - 2 = 433 is prime.

%t Select[Range[700], PrimeQ[#]&&(PrimeQ[t=#(#+1)/2+1]||PrimeQ[t-3]) &]

%Y Cf. A000040 (supersequence), A000124, A000217, A034856.

%Y Complement of A376205 in A000040.

%K nonn,easy

%O 1,1

%A _Stefano Spezia_, Sep 15 2024