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

1,1

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.

Links

Table of n, a(n) for n=1..55.

Example

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

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]

Crossrefs

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

Sequence in context: A368374 A004769 A224380 * A158290 A328896 A057538

Adjacent sequences: A125768 A125769 A125770 * A125772 A125773 A125774

Keyword

nonn

Author

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

Status

approved