A279756 -id:A279756 - cp's OEIS frontend

A343908 a(n) is the least prime == 4 (mod prime(n)).

2, 7, 19, 11, 37, 17, 89, 23, 73, 149, 97, 41, 127, 47, 239, 163, 181, 431, 71, 359, 223, 83, 419, 271, 101, 307, 107, 967, 113, 569, 131, 397, 1237, 421, 2239, 457, 1103, 167, 839, 523, 541, 547, 577, 197, 1777, 601, 1481, 227, 3863, 233, 3499, 2633, 727, 757, 1289, 1319, 811, 1901, 281, 1409

Offset: 1

Zak Seidov, May 03 2021

nonn

			a(3) = 19 because 19 is the least prime == 4 (mod prime(3)).
a(4) = 11 because 11 is the least prime == 4 (mod prime(4)).

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000040, A023200 (primes p such that p+4 is also prime), A034694, A035095, A279756.

a:= proc(n) local q, p; p:= ithprime(n); q:= p;
      do if irem(q-4, p)=0 then break fi;
         q:= nextprime(q);
      od; q
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, May 03 2021

s = {}; p = 5; Do[q = p + 2; While[Mod[q, p] != 4, q = NextPrime[q]]; AppendTo[s, q]; p = NextPrime[p], {100}]; s

a(n) = my(p=prime(n)); forprime(q=2,, if (Mod(q, p) == 4, return(q))); \\ Michel Marcus, May 03 2021

A367805 a(1) = 0; for n > 1, a(n) is the least positive integer k for which k*prime(n) + 2 is prime.

Original entry on oeis.org

0, 1, 1, 3, 1, 3, 1, 3, 3, 1, 5, 3, 1, 3, 7, 7, 1, 5, 5, 1, 5, 3, 3, 3, 3, 1, 3, 1, 5, 9, 3, 7, 1, 3, 1, 5, 5, 3, 3, 3, 1, 5, 1, 5, 1, 3, 9, 5, 1, 9, 3, 1, 15, 7, 3, 15, 1, 9, 11, 1, 9, 3, 21, 1, 3, 3, 5, 3, 1, 3, 3, 15, 3, 5, 9, 3, 13, 3, 19, 3, 1, 15, 1, 3, 3, 9, 13, 3, 1, 15

Offset: 1

Frank Hollstein, Dec 01 2023

nonn

			For n = 4: a(4) = 3, because prime(4) = 7, 3*7 + 2 = 23 which is prime.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000040, A029707, A035096, A117673, A279756, A001359.

a:= proc(n) local p, q, r; p:= ithprime(n); q:= p;
      while irem(q-2, p, 'r')<>0 do q:= nextprime(q) od; r
    end:
seq(a(n), n=1..99);  # Alois P. Heinz, Dec 04 2023

nmax=90; a[1]=0; For[n=2, n<=nmax, n++, For[k=1, k>0, k++, If[PrimeQ[k*Prime[n]+2], a[n]=k; k=-1]]]; Array[a,nmax] (* Stefano Spezia, Dec 04 2023 *)

a(n) = if (n==1, 0, my(k=1, p=prime(n)); while (!isprime(k*p+2), k++); k); \\ Michel Marcus, Dec 02 2023

from itertools import count, dropwhile
from sympy import prime, isprime
def A367805(n):
    if n==1:
        return 0
    else:
        p = prime(n)
        return next(dropwhile(lambda x:not isprime(x*p+2),count(1))) # Chai Wah Wu, Jan 04 2024

a(n) = (A279756(n) - 2)/A000040(n).

a(n) = 1 <=> n in A029707.

More terms from Michel Marcus, Dec 02 2023

cp's OEIS Frontend

A343908 a(n) is the least prime == 4 (mod prime(n)).

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