A125771 Primes of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 9.

11, 19, 29, 31, 37, 41, 43, 59, 61, 67, 71, 73, 79, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 167, 179, 181, 191, 197, 199, 211, 223, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281, 293, 307, 311, 313, 331, 337, 349, 359, 379, 389, 397

Offset: 1

Author

Jonathan Vos Post & Robert G. Wilson v, Dec 05 2006

Keywords

• nonn

Comments

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.

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.

Examples

			11 = 1*10 +1,
19 = 2*10 -1, etc.
		

Crossrefs

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

Programs

Mathematica

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]