A061671 Numbers n such that { x +- 2^k : 0 < k < 4 } are primes, where x = 210*n - 105.

1, 77, 93, 209, 5197, 7695, 9307, 13442, 13524, 15445, 16192, 28600, 30970, 34228, 36388, 38391, 41625, 50127, 52795, 55546, 69146, 70538, 70642, 70747, 76314, 76642, 90079, 91416, 93496, 94288, 95773, 96415, 101530, 104049, 107559, 118031

Offset: 1

Author

Frank Ellermann, Jun 16 2001

Keywords

• nonn

Comments

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

Examples

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

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..900
• F. Ellermann, Illustration for A002110, A005867, A038110, A060753

Crossrefs

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

Programs

Mathematica

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

Extensions

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.