A239727 -id:A239727 - cp's OEIS frontend

A342364 The primes associated with A239727.

3, 17, 73, 191, 709, 1289, 3181, 5449, 7681, 17477, 33889, 87961, 437389, 2290573, 7160227, 10429681, 19196227, 24504049, 47577857, 70513979, 82605937, 156671243, 271785793, 328939937, 568119509, 1125978241, 1534657963, 1710749497, 4936728373, 7647104183

Offset: 1

Jianing Song, Mar 09 2021

nonn

			The smallest prime of the form 2*A239727(3)*k + 1 = 24*k+1 is 73, hence a(3) = 73.
The smallest prime of the form 2*A239727(4)*k + 1 = 38*k+1 is 191, hence a(4) = 191.

Jianing Song, Table of n, a(n) for n = 1..40

Cf. A239727, A239746, A016014, A070846, A342365.

A016014(n)=my(k); while(!isprime(2*n*k+++1), ); k
r=0; for(n=1, 1e8, t=A016014(n); if(t>r, r=t; print1(2*n*r+1", "))) \\ based on the program of A239727

a(n) = 2*A239727(n)*A239746(n) + 1.

A016014 Least k such that 2nk + 1 is a prime.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 3, 3, 1, 5, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 5, 3, 1, 2, 1, 1, 2, 3, 1, 3, 1, 4, 2, 1, 2, 3, 3, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 2, 6, 2, 3, 3, 1, 2, 1, 3, 2, 1, 1, 2, 4, 3, 2, 1, 1, 3, 3, 1, 2, 4, 1, 5, 1, 2, 6, 1, 2, 2, 1, 1, 3, 7, 2, 5, 1, 1, 2, 1, 1

Offset: 1

Robert G. Wilson v

nonn

Is the sequence bounded? - Zak Seidov, Mar 25 2014
Answer: No, for any given N a number n such that a(n) > N can be constructed by the Chinese Remainder Theorem, see A239727. - Charles R Greathouse IV, Mar 25 2014
a(n) = 1 for n in A005097. - Robert Israel, Oct 26 2016

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A005097, A103961.
A070846 contains the corresponding primes.
Records are in A239746 with indices in A239727.

f:= proc(n) local k;
     for k from 1 do if isprime(2*n*k+1) then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Oct 26 2016

Do[k = 1; cp = n*k + 1; While[ ! PrimeQ[cp], k++; cp = n*k + 1]; Print[k], {n, 2, 400, 2}] (* Lei Zhou, Feb 23 2005 *)
lk[n_]:=Module[{k=1},While[!PrimeQ[2n k+1],k++];k]; Array[lk,100] (* Harvey P. Dale, Apr 23 2023 *)

a(n)=my(k); while(!isprime(2*n*(k++)+1),);k \\ Charles R Greathouse IV, Mar 25 2014

from sympy import isprime
def a(n):
    k = 1
    while not isprime(2*n*k + 1): k += 1
    return k
print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Mar 28 2022

A239746 Records in A016014.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 12, 15, 17, 24, 30, 42, 54, 57, 60, 63, 72, 74, 83, 84, 91, 96, 104, 106, 120, 123, 129, 138, 139, 144, 147, 149, 153, 155, 203, 219, 240, 245, 259

Offset: 1

Zak Seidov, Mar 26 2014

Cf. A016014, A239727.

km = 0; Reap[Do[k = 1;  While[ ! PrimeQ[2*n*k + 1], k++]; If[k > km, km = k; Sow[k]], {n,  20000}]][[2, 1]]
lk[n_]:=Module[{k=1},While[!PrimeQ[2n k+1],k++];k];DeleteDuplicates[Array[ lk,10^7],GreaterEqual] (* Harvey P. Dale, Jun 20 2023 *)

A016014(n)=my(k); while(!isprime(2*n*k+++1), ); k
r=0; for(n=1, 1e8, t=A016014(n); if(t>r, r=t; print1(r", "))) \\ Jianing Song, Mar 09 2021, based on the program of A239727

a(37)-a(40) from Giovanni Resta, Mar 26 2014

A239800 First appearance of n in A016014, or 0 if n never occurs.

Original entry on oeis.org

1, 4, 12, 42, 19, 59, 92, 196, 184, 159, 334, 227, 317, 415, 256, 521, 514, 796, 734, 1861, 1691, 1997, 2053, 706, 5006, 5731, 3814, 2348, 5641, 1466, 19016, 5542, 26815, 8762, 18637, 5794, 31667, 5227, 17054, 35246, 51148, 5207, 59537, 75862, 54737, 117899, 58603, 81313, 30332, 100042, 205471, 113018, 102307, 21209, 63971, 321994, 62809, 648512

Offset: 1

Zak Seidov, Mar 27 2014

nonn

Conjecture: a(n) > 0 for all n. - Jianing Song, Mar 09 2021

Zak Seidov, Table of n, a(n) for n = 1..100

Cf. A016014, A239746, A239727.

isA239800 := proc(n, m) local k;
for k from 1 to n-1 while not isprime(2*m*k + 1) do od;
if k < n then false else isprime(2*m*n + 1) fi end:
A239800 := proc(n, SearchLimit) local k;
for k from 1 to SearchLimit do if isA239800(n, k) then return k fi od;
error "Search limit reached!" end:
A239800List := (ListLength, SearchLimit) ->
map(n -> A239800(n, SearchLimit), [$1..ListLength]):
A239800List(32, 65537); # Peter Luschny, Oct 05 2021

A016014(a(n)) = n.

Escape clause added by Jianing Song, Mar 09 2021

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A342364 The primes associated with A239727.

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A016014 Least k such that 2*n*k + 1 is a prime.

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A239746 Records in A016014.

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A239800 First appearance of n in A016014, or 0 if n never occurs.

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A016014 Least k such that 2nk + 1 is a prime.