A162864 - OEIS

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A162864

Integers n, divisible by six, for which t = (4^n - 5 * 2^n - 4 * 4^(n^2 - 2n) + 8 * 2^(n^2 - 2n)) / (4 * (n^3 - n)) is an integer

6, 12, 18, 30, 36, 42, 60, 72, 108, 180, 192, 240, 270, 312, 420, 432, 462, 600, 660, 810, 882, 1092, 1152, 1290, 1296, 1302, 1320, 1620, 1722, 1872, 2028, 2112, 2268, 2310, 2340, 2592, 2688, 2700, 2790, 2970, 3000, 3120, 3258, 3300, 3360, 3390, 3528, 3540

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Then n - 1 and n + 1 are almost always a pair of twin primes, and the set of these should be an infinite subset of all twin primes.

If n - 1 and n + 1 are simultaneously composite, this occurs very rarely.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..100

MATHEMATICA

Select[6*Range[600], IntegerQ[(4^#-5*2^#-4*4^(#^2-2#)+8*2^(#^2-2#))/(4*(#^3-#))]&] (* Harvey P. Dale, Dec 31 2024 *)

CROSSREFS

Cf. A001097