A162865 -id:A162865 - cp's OEIS frontend

A092660 Number of consecutive prime runs of 9 primes congruent to 1 mod 4 below 10^n.

0, 0, 0, 0, 1, 6, 71, 851, 8919, 90049, 894724

Offset: 1

Enoch Haga, Mar 02 2004

			a(6)=6 because 6 sets of 9 primes occur below 10^6, each run interrupted by a prime congruent to 3 mod 4.

Cf. A092661 A092662.

Cf. A162865. [From Rick L. Shepherd, Jul 15 2009]

Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 9 primes occur before interruption by a prime congruent to 3 mod 4.

a(9) from Rick L. Shepherd, Jul 15 2009
a(10) from Sean A. Irvine, Oct 25 2011
a(11) from Chai Wah Wu, Mar 18 2018

A162866 Initial prime of exactly nine consecutive primes congruent to 3 modulo 4.

Original entry on oeis.org

39607, 278051, 339863, 341827, 402371, 519587, 735211, 919423, 1123219, 1191643, 1263239, 1329763, 1635547, 1648919, 1737863, 1994119, 2191687, 2465227, 2566279, 3025423, 3101743, 3197899, 3306731, 3719467, 4259243, 4466411, 4498883, 4591507, 4680503, 5031863

Offset: 1

Rick L. Shepherd, Jul 15 2009

The table provides all 8949 [=A092661(9)] terms less than 10^9.

If 10 or more consecutive primes are all congruent to 3 modulo 4, none of them is a member of this sequence. - Harvey P. Dale, Oct 23 2011

Rick L. Shepherd, Table of n, a(n) for n=1..8949

Cf. A092661, A162865, A055624, A057619, A054678.

m9Q[l_]:=Module[{ms=Mod[l,4]},First[ms]!=3&&Last[ms]!=3&&Union[ Take[ ms,{2,10}]]=={3}]; Transpose[Select[Partition[Prime[Range[ 320000]], 11,1],m9Q]][[2]] (* Harvey P. Dale, Oct 23 2011 *)

cp's OEIS Frontend

A092660 Number of consecutive prime runs of 9 primes congruent to 1 mod 4 below 10^n.

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A162866 Initial prime of exactly nine consecutive primes congruent to 3 modulo 4.

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