The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A092645 Number of consecutive prime runs of just 4 primes congruent to 1 mod 4 below 10^n. 2
 0, 0, 2, 10, 124, 1047, 8756, 78845, 703152, 6387276, 58448789 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: a(n) ~ 10^n / (64 log 10 * n). - Charles R Greathouse IV, Oct 24 2011 LINKS 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: A060690 A013038 A005321 * A333455 A334555 A202950 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 20:15 EST 2020. Contains 338854 sequences. (Running on oeis4.)