A072063 -id:A072063 - cp's OEIS frontend

A072064 Least k>0 such that prime(n)+k*n is prime.

1, 1, 2, 1, 4, 1, 2, 3, 2, 3, 2, 2, 2, 2, 4, 3, 4, 1, 6, 3, 4, 1, 10, 1, 4, 1, 2, 2, 2, 2, 4, 1, 4, 1, 6, 2, 6, 2, 6, 3, 24, 1, 2, 2, 6, 3, 8, 1, 6, 3, 8, 5, 2, 2, 2, 3, 2, 4, 6, 2, 16, 3, 2, 2, 2, 1, 4, 3, 6, 1, 10, 1, 4, 2, 6, 6, 16, 3, 8, 2, 4, 1, 6, 2, 10, 3, 4, 4, 18, 2, 6, 1, 2

Offset: 1

Reinhard Zumkeller, Jun 12 2002

nonn

			n=3, prime(3)=5: 5+1*3=8 is not prime, but 5+2*3=11, therefore a(3)=2 and A072063(3)=11.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A034693, A000040, A072063.

A072064[n_]:=Module[{p=Prime[n],k=1},While[!PrimeQ[p+k*n],k++];k];Array[A072064,100] (* Paolo Xausa, Nov 27 2023 *)

a(n) = my(p=prime(n), k=1); while (!isprime(p+k*n), k++); k; \\ Michel Marcus, Nov 27 2023

A090471 Smallest prime not already used that is of the form prime(n)+kn for some k > 0.

Original entry on oeis.org

3, 5, 11, 19, 31, 37, 59, 43, 41, 79, 53, 61, 67, 71, 107, 101, 127, 97, 181, 131, 157, 167, 313, 113, 197, 179, 211, 163, 283, 173, 251, 227, 269, 241, 359, 223, 379, 239, 401, 293, 1163, 307, 277, 281, 467, 337, 587, 271, 521, 479, 641, 499, 347, 683, 367, 431

Offset: 1

Amarnath Murthy, Dec 02 2003

nonn

Cf. A072063.

More terms from David Wasserman, Nov 08 2005

A359273 a(n) = least positive integer k such that (prime(n+k)-prime(n))/n is an integer.

Original entry on oeis.org

1, 1, 2, 1, 6, 2, 4, 6, 4, 7, 5, 6, 6, 6, 13, 10, 14, 4, 23, 12, 16, 4, 42, 6, 20, 5, 10, 10, 10, 10, 23, 6, 24, 6, 37, 12, 38, 14, 40, 22, 151, 6, 16, 16, 46, 22, 60, 10, 49, 25, 65, 43, 16, 18, 18, 27, 19, 38, 56, 19, 144, 30, 21, 21, 21, 10, 42, 32, 66

Offset: 1

Clark Kimberling, Jan 26 2023

nonn

			a(5) = 6 because 5 divides 20, which is prime(5+6) - prime(5), and if 0 < k < 6, then 5 does not divide prime(5+k) - prime(5).

Cf. A000040, A072063.

f:= proc(n) local p,k,q;
  p:= ithprime(n); q:= p;
  for k from 1 do
    q:= nextprime(q);
    if (q - p) mod n = 0 then return k fi;
  od
end proc:
map(f, [$1..100]); # Robert Israel, Jan 26 2023

p[n_] := Prime[n];
a[n_] := Select[Range[1000], IntegerQ[(p[n + #] - p[n])/n] &, 1]
Flatten[Table[a[n], {n, 1, 130}]]

cp's OEIS Frontend

A072064 Least k>0 such that prime(n)+k*n is prime.

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A090471 Smallest prime not already used that is of the form prime(n)+kn for some k > 0.

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A359273 a(n) = least positive integer k such that (prime(n+k)-prime(n))/n is an integer.

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