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

1,2

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.

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A052202 A089525 A274172 * A269809 A064902 A247682

Adjacent sequences: A061668 A061669 A061670 * A061672 A061673 A061674

Keyword

nonn

Author

Frank Ellermann, Jun 16 2001

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.

Status

approved