A216312 The prime ending in 9 is the only prime in a decade.

149, 419, 479, 719, 809, 839, 929, 1009, 1049, 1249, 1259, 1319, 1399, 1409, 1709, 1889, 1949, 2039, 2099, 2129, 2179, 2309, 2459, 2579, 2609, 2729, 2789, 2819, 2879, 2939, 2999, 3079, 3109, 3119, 3299, 3359, 3389, 3449, 3659, 3719, 3779, 3989, 4049, 4229

Offset

1,1

Comments

Primes of the form 10n+9 such that 10n+1, 10n+3, and 10n+7 are composite. - Charles R Greathouse IV, Sep 06 2012

Links

V. Raman, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012

Example

149 is prime but 141, 143 and 147 are all composite (being 3 * 47, 11 * 13 and 3 * 7^2 respectively), thus 149 is in the sequence.

Mathematica

Select[Prime[Range[700]], Mod[#, 10] == 9 && Union[PrimeQ[{# - 8, # - 6, # - 2}]] == {False} &] (* Alonso del Arte, Sep 03 2012 *)
Select[Table[10n+{1, 3, 7, 9}, {n, 450}], Boole[PrimeQ[#]]=={0, 0, 0, 1}&][[;; , 4]] (* Harvey P. Dale, Mar 08 2023 *)

Prog

(Magma) [p: p in PrimesUpTo(4300) | p mod 10 eq 9 and IsOne(#PrimesInInterval(10*t+1, 10*t+9)) where t is Floor(p/10)]; // Bruno Berselli, Sep 14 2012

Crossrefs

Subsequence of A030433. Cf. A032352, A007811, A078494, A030433.

Sequence in context: A095842 A142359 A185692 * A112859 A141980 A023290

Adjacent sequences: A216309 A216310 A216311 * A216313 A216314 A216315

Keyword

nonn,base,easy

Author

V. Raman, Sep 03 2012

Status

approved