A125771 - OEIS

%I #5 Mar 30 2012 18:40:42

%S 11,19,29,31,37,41,43,59,61,67,71,73,79,83,89,101,107,109,113,127,131,

%T 137,139,149,151,157,167,179,181,191,197,199,211,223,229,233,239,241,

%U 251,263,269,271,277,281,293,307,311,313,331,337,349,359,379,389,397

%N Primes of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 9.

%C Since all primes would eventually appear in A125765 or A125766 because (p +/-1) times 1(1+1)/2 equals (p +/- 1) let us not use the first triangular number 1.

%C Primes not of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 1 only produces one prime: 3. If we restrict triangular numbers greater than 5, then only two primes are found: 2 & 3.

%e 11 = 1*10 +1,

%e 19 = 2*10 -1, etc.

%t s = {}; Do[m = j*k*(k + 1)/2; If[ PrimeQ[m - 1], AppendTo[s, m - 1]]; If[ PrimeQ[m + 1], AppendTo[s, m + 1]], {j, 40}, {k, 4, 23}]; Take[ Union@s, 75]

%Y Cf. A000217, A125765, A125766, A125767, A125768, A125769, A125770.

%K nonn

%O 1,1

%A _Jonathan Vos Post_ & _Robert G. Wilson v_, Dec 05 2006