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A247384 Find the first (maximal) string of consecutive primes of length exactly n which alternate between 4*k+1 and 4*k+3 or 4*k+3 and 4*k+1 as in A002144(4*n+1) and A002145(4*n+3). The first element is a(n). 3
97, 11, 3, 23, 47, 167, 131, 2011, 233, 23633, 34499, 1013, 9341, 90659, 521, 51749, 505049, 1391087, 2264839, 2556713, 17123893, 2569529, 15090641, 18246451, 6160043, 1557431471, 43679609, 198572029, 701575297, 5552898499, 6639843979, 61233611783, 9005520203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Jens Kruse Andersen and Giovanni Resta, Table of n, a(n) for n = 1..45 (first 38 terms from Jens Kruse Andersen)

Jens Kruse Andersen, Consecutive Congruent Primes

FORMULA

a(n) = A289118(n) if and only if n > 1 and A289118(n) < A289118(n+1). - Jonathan Sondow, Jun 27 2017

EXAMPLE

a(4)=23 because 23,29,31,37 alternate 4*n+3,4*n+1,4*n+3,4*n+1 for exactly four primes and 23 is the least prime for a string of exactly four.

MAPLE

Primes:= select(isprime, [seq(2*i+1, i=1..10^7)]):

Pm4:= map(`modp`, [seq((-1)^j*Primes[j], j=1..nops(Primes))], 4):

Starts:= [1, op(select(t -> Pm4[t-1]<> Pm4[t], [$2..nops(Pm4)]))]:

Lengths:= [seq(Starts[i+1]-Starts[i], i=1..nops(Starts)-1)]:

for i from 1 to max(Lengths) do A[i]:= ListTools:-Search(i, Lengths) od:

R:=[seq(A[i], i=1..max(Lengths))]:

seq(`if`(a=0, 0, Primes[Starts[a]]), a=R); # Robert Israel, Sep 15 2014

MATHEMATICA

i = 2; While[ Mod[ Prime[i] - Prime[i - 1], 4] != 0 || Mod[ Prime[i + 1] - Prime[i], 4] != 0, i++]; T = {Prime[i]}; Do[j = 2; While[! (Product[ Mod[ Prime[k + 1] - Prime[k], 4], {k, j, j + n}] != 0 && (Mod[Prime[j] - Prime[j - 1], 4] == 0 || j == 2) && Mod[ Prime[j + n + 2] - Prime[j + n + 1], 4] == 0), j++]; T = Append[T, Prime[j]], {n, 0, 13}]; T (* Jonathan Sondow, Jun 28 2017 *)

PROG

(PARI) v=vector(100); v[1]=7; cur=1; p=3; forprime(q=5, 1e10, if((q-p)%4==0, if(!v[cur], v[cur]=back(p, cur); print("a("cur") = "v[cur])); cur=1, cur++); p=q) \\ Charles R Greathouse IV, Sep 15 2014

CROSSREFS

Cf. A002144, A002145, A098058, A098059, A289118, A289237.

Sequence in context: A051330 A106429 A126840 * A094498 A068830 A033417

Adjacent sequences:  A247381 A247382 A247383 * A247385 A247386 A247387

KEYWORD

nonn

AUTHOR

J. M. Bergot, Sep 15 2014

EXTENSIONS

More terms from Jens Kruse Andersen, Oct 01 2014

Definition clarified by Jonathan Sondow, Jun 25 2017

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)