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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 October 15 18:18 EDT 2019. Contains 328037 sequences. (Running on oeis4.)