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Numbers n such that { x +- 2^k : 0 < k < 4 } are primes, where x = 210*n - 105.
4

%I #12 Feb 05 2019 13:29:36

%S 1,77,93,209,5197,7695,9307,13442,13524,15445,16192,28600,30970,34228,

%T 36388,38391,41625,50127,52795,55546,69146,70538,70642,70747,76314,

%U 76642,90079,91416,93496,94288,95773,96415,101530,104049,107559,118031

%N Numbers n such that { x +- 2^k : 0 < k < 4 } are primes, where x = 210*n - 105.

%C This sequence does not include the sextet (7,11,13,17,19,23). It is a proper subset of A014561 in a certain sense.

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, conjectures following th. 5

%H Harvey P. Dale, <a href="/A061671/b061671.txt">Table of n, a(n) for n = 1..900</a>

%H F. Ellermann, <a href="/A005867/a005867.txt">Illustration for A002110, A005867, A038110, A060753</a>

%e 16057, 16061, 16063, 16067, 16069, 16073 are prime and (16065+105)/210= 77= a(2).

%t Select[Range[1, 1000000], Union[PrimeQ[(210*# - 105) + {-8, -4, -2, 2, 4, 8}]] == {True} &]

%t Select[Range[120000],AllTrue[210#-105+{-8,-4,-2,2,4,8},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 05 2019 *)

%Y 210 = 7*5*3*2 = A002110(4), cf. A014561.

%K nonn

%O 1,2

%A _Frank Ellermann_, Jun 16 2001

%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 20 2001 and from _Frank Ellermann_, Nov 26 2001. Mathematica script from Peter Bertok (peter(AT)bertok.com), Nov 27 2001.