

A306362


Prime numbers in A317298.


1



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
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OFFSET

1,1


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


LINKS

Table of n, a(n) for n=1..42.


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A188382, A317298, A304487.
Sequence in context: A069358 A108544 A095088 * A007138 A046107 A243110
Adjacent sequences: A306359 A306360 A306361 * A306363 A306364 A306365


KEYWORD

nonn


AUTHOR

Stefano Spezia, Feb 10 2019


STATUS

approved



