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A125771 Primes of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 9. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A032694 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

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Last modified December 6 16:37 EST 2021. Contains 349567 sequences. (Running on oeis4.)