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.
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
KEYWORD
nonn
AUTHOR
Jonathan Vos Post & Robert G. Wilson v, Dec 05 2006
STATUS
approved