A145986 n-th prime in the first occurrence of at least n consecutive primes of the form 4k + 1.

5, 17, 101, 409, 2633, 11657, 11677, 11681, 11689, 373777, 766373, 3358373, 12205121, 12270281, 12270301, 12270317, 297388097, 297779509, 297779513, 1113443473, 1113443521, 1113443533, 1113443549, 1113443561, 84676453373, 84676453429

Offset

1,1

Comments

a(1)=5 is same as A055623(1) because 5 is a single-digit number.

References

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

Links

Table of n, a(n) for n=1..26.

Example

a(2)=17 because this is the 2nd prime in the first run of 2 primes where p == 1 mod 4.

Mathematica

Flatten[Table[SequencePosition[Table[If[Mod[p-1, 4]==0, 1, 0], {p, Prime[Range[250000]]}], PadRight[ {}, n, 1], 1], {n, 12}], 1][[;; , -1]]//Prime (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jul 14 2024 *)

Prog

(UBASIC) 10 'cluster primes
20 C=1: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: E=int(N/4):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: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
(PARI) r=0; c=0; forprime(p=2, 4e9, if(p%4==1, if(c++>r, r=c; print1(p", ")), c=0)) \\ Charles R Greathouse IV, Mar 22 2011

Crossrefs

Cf. A055623, A054624, A145988, A145989, A145990, A145991, A145992, A145993, A145994.

Sequence in context: A139390 A145824 A076516 * A375424 A200992 A034821

Adjacent sequences: A145983 A145984 A145985 * A145987 A145988 A145989

Keyword

nonn

Author

Enoch Haga, Oct 26 2008

Extensions

Entry rewritten and a(13)-a(26) added by Charles R Greathouse IV, Mar 22 2011

Edited by M. F. Hasler, May 02 2015

Definition clarified by N. J. A. Sloane, Dec 18 2022

Status

approved