A092645 Number of consecutive prime runs of just 4 primes congruent to 1 mod 4 below 10^n.

0, 0, 2, 10, 124, 1047, 8756, 78845, 703152, 6387276, 58448789

Offset

1,3

Comments

Conjecture: a(n) ~ 10^n / (64 log 10 * n). - Charles R Greathouse IV, Oct 24 2011

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 4 primes occur before interruption by a prime congruent to 3 mod 4.

Example

a(5)=124 because 124 sets of 4 primes occur below 10^5, each run interrupted by a prime congruent to 3 mod 4.

Mathematica

p1 = p3 = 0; p = 15; s = Mod[{2, 3, 5, 7, 11, 13}, 4]; Do[ While[p < 10^n, If[s == {3, 1, 1, 1, 1, 3}, p1++]; If[s == {1, 3, 3, 3, 3, 1}, p3++]; p = NextPrime@ p; s = Join[ Take[s, -5], {Mod[p, 4]}]]; Print[{p1, p3}], {n, 2, 9}] (* Robert G. Wilson v, Sep 30 2011 *)

Prog

(PARI) a(n)=my(s, t); forprime(p=2, nextprime(10^n), if(p%4==1, t++, s+=t==4; t=0)); s \\ Charles R Greathouse IV, Oct 24 2011

Crossrefs

Cf. A092646, A092647.

Sequence in context: A005321 A339934 A348876 * A346372 A333455 A372316

Adjacent sequences: A092642 A092643 A092644 * A092646 A092647 A092648

Keyword

more,nonn

Author

Enoch Haga, Mar 02 2004

Extensions

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

Status

approved