A306362 Prime numbers in A317298.

3, 11, 37, 79, 137, 211, 821, 991, 1597, 1831, 2081, 2347, 2927, 3571, 3917, 4657, 5051, 6329, 8779, 9871, 11027, 14197, 14879, 17021, 20101, 21737, 26107, 27967, 28921, 33931, 34981, 39341, 40471, 41617, 50087, 51361, 59341, 60727, 62129, 66431, 69379, 70877

Offset: 1

Author

Stefano Spezia, Feb 10 2019

Keywords

• nonn

Comments

Conjecture: Except the first term a(1) = 3, all the other terms do not end with 3.

It is easy to prove that the numbers A317298(n) end with 3 only when n ends with 1. In this case A317298(10*n+1) = (10*n + 1)*(20*n + 3), which is composite for n > 0. Therefore the conjecture is true. - Bruno Berselli, Feb 11 2019

Essentially (apart from the 3) the same as A188382, because for even n, A317298(n=2k) has the form 1+2*k+8*k^2 and for odd n A317298(n) is a multiple of n and not prime. - R. J. Mathar, Feb 14 2019

Crossrefs

Cf. A188382, A317298, A304487.

Programs

Mathematica

Select[Table[(1/2)*(1 + (-1)^n + 2*n + 4*n^2),{n,1,300}], PrimeQ]

PARI

for(n=0, 300, if(ispseudoprime(t=(1/2)*(1 + (-1)^n + 2*n + 4*n^2)), print1(t", ")));