A145989 Run lengths of consecutive primes == 1 (mod 4) where the run length is at least 2.

2, 2, 3, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 3, 2, 4, 2, 2, 2, 3, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 5, 2, 3, 2, 2, 2, 2, 2

Offset: 1

Author

Enoch Haga, Oct 26 2008

Keywords

• easy
• nonn

Comments

The run lengths of 1's in A039702 are 1, 2, 1, 2, 1, 1, 1, 3,.. as listed in A091318. Deleting all 1's from A091318 generates this sequence here. - R. J. mathar, Sep 30 2011

The maximum run length in the first 1000 terms is 9. - Harvey P. Dale, Jul 27 2025

Examples

			a(1)=2 because this sequence includes consecutive runs of any length and this first occurrence > 1 is a run of 2.
		

References

• Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055623, A054624, A145986, A145988 - A145994.

Programs

Mathematica

Length/@Select[Split[Table[If[Mod[p,4]==1,1,0],{p,Prime[Range[500]]}]],#[[1]]==1&&Length[#]>1&] (* Harvey P. Dale, Jul 27 2025 *)

UBASIC

10 'cluster primes
20 C=1
30 input "end #";L
40 for N=3 to L step 2
50 S=int(sqrt(N))
60 for A=3 to S step 2
70 B=N/A
80 if int(B)*A=N then cancel for:goto 170
90 next A
100 C=C+1
110 E=N/4:E=int(E):R=N-(4*E)
120 if R=1 then print N;:C1=C1+1:T1=T1+1:print T1
130 if R=3 then T1=0
140 if R=3 then print " ";N;:C3=C3+1:T2=T2+1:print T2
150 if R=1 then T2=0
160 if T1>10 or T2>10 then stop
170 next
180 print "Total primes=";C;:print "Type A";C1;"Type B";C3