A086135 Numbers n such that n and n+10 are both prime but are non-consecutive; which means that at least one prime is between n and n+10; it is not identical with A023303 because here the terms of A031928 are missing.

3, 7, 13, 19, 31, 37, 43, 61, 73, 79, 97, 103, 127, 157, 163, 223, 229, 271, 307, 349, 373, 379, 433, 439, 457, 499, 607, 643, 673, 733, 751, 853, 877, 937, 967, 1009, 1087, 1093, 1213, 1279, 1291, 1297, 1423, 1429, 1483, 1489, 1543, 1549, 1597, 1609, 1657, 1777

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Complement of a=A031928 with respect to b=A023303: [b]&[nota]: this and A031928 are disjoint, but A031928 is a proper subset of A023303.

Example

First deviation from A023303 = {3,7,13,19,31,37,43,61,73,79,97,103,127,139,157,..} is due to the absence of 139=A031928(1).

Mathematica

Do[s=Prime[n]; s1=Prime[n+1]; If[PrimeQ[s+d]&& !Equal[s1-s, d], Print[s]], {n, 1, 1000}]
Select[Prime[Range[300]], PrimeQ[#+10]&&NextPrime[#]!=(#+10)&] (* Harvey P. Dale, Oct 25 2020 *)

Crossrefs

Sequence in context: A215809 A015916 A023203 * A023220 A207990 A023205

Adjacent sequences: A086132 A086133 A086134 * A086136 A086137 A086138

Keyword

nonn

Author

Labos Elemer, Jul 28 2003

Status

approved