A092642 Number of consecutive prime runs of 3 primes congruent to 1 mod 4 below 10^n.

0, 0, 4, 38, 305, 2450, 20939, 182955, 1618599, 14491882, 131026137

Offset

1,3

Links

Table of n, a(n) for n=1..11.

Formula

Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 3 primes occur before interruption by a prime congruent to 3 mod 4.

Example

a(5)=305 because 305 sets of 3 primes occur below 10^5, each run interrupted by a prime congruent to 3 mod 4.

Mathematica

A002145 = Join[{0}, Select[4 Range[0, 10^4] + 3, PrimeQ[#] &]];
A002144 = Select[4 Range[0, 10^4] + 1, PrimeQ[#] &];
lst = {}; Do[If[Length[s = Select[A002144, Between[{A002145[[i]], A002145[[i + 1]]}]]] == 3, AppendTo[lst, Last[s]]], {i, Length[A002145] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}]  (* Robert Price, Jun 09 2019 *)

Crossrefs

Cf. A092643, A092644.

Sequence in context: A196702 A196945 A240287 * A020865 A240378 A220807

Adjacent sequences: A092639 A092640 A092641 * A092643 A092644 A092645

Keyword

more,nonn

Author

Enoch Haga, Mar 02 2004

Extensions

a(9)-a(11) from Chai Wah Wu, Mar 18 2018

Status

approved