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A092637 Number of consecutive prime runs of 1 prime congruent to 3 mod 4 below 10^n. 4
1, 3, 28, 217, 1570, 12515, 102942, 867677, 7541800, 66571277, 595524791 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 one prime occurs before interruption by a prime congruent to 1 mod 4.

EXAMPLE

a(3)=28 because 28 single primes occur below 10^3, each interrupted in the run by a prime congruent to 1 mod 4.

MATHEMATICA

A002144 = Join[{0}, Select[4 Range[0, 10^4] + 1, PrimeQ[#] &]];

A002145 = Select[4 Range[0, 10^4] + 3, PrimeQ[#] &];

lst = {}; Do[If[Length[s = Select[A002145, Between[{A002144[[i]], A002144[[i + 1]]}]]] == 1, AppendTo[lst, Last[s]]], {i, Length[A002144] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}] (* Robert Price, May 31 2019 *)

CROSSREFS

Cf. A091318, A092636 - A092665.

Sequence in context: A045737 A003466 A337590 * A338689 A094296 A172241

Adjacent sequences: A092634 A092635 A092636 * A092638 A092639 A092640

KEYWORD

more,nonn

AUTHOR

Enoch Haga, Mar 02 2004

EXTENSIONS

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

STATUS

approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)