A092639 Number of consecutive prime runs of 2 primes congruent to 1 mod 4 below 10^n.

0, 2, 14, 116, 780, 6066, 49510, 417230, 3631524, 32070665, 287366058

Offset: 1

Author

Enoch Haga, Mar 02 2004

Keywords

• more
• nonn

Examples

			a(4)=116 because 116 pairs of primes occur below 10^4, each run interrupted by a prime congruent to 3 mod 4.
		

Crossrefs

Cf. A092640, A092641.

Programs

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]]}]]] == 2, AppendTo[lst, Last[s]]], {i, Length[A002145] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}]  (* Robert Price, Jun 09 2019 *)

PARI

ispRun(p1)={ local(p2,p3) ; if(!isprime(p1) || (p1 %4 ==3) || (precprime(p1-1) % 4 ==1), return(0), p2=nextprime(p1+1) ; if( p2 %4 == 3, return(0), p3=nextprime(p2+1) ; if( p3 %4 == 3, return(1), return(0) ) ; ) ; ) ; } { an=0 ; n=1 ; p=prime(1) ; while(1, if( (p<10^n) && (nextprime(p+1) >= 10^n), print(an); n++ ; ) ; an += ispRun(p) ; p=nextprime(p+1) ; ) } \\ R. J. Mathar, Sep 25 2006

Formula

Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 2 primes occur before interruption by a prime congruent to 3 mod 4.

Extensions

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