A178984 a(n) is the smallest prime p that makes prime(n) + 1 - p a prime.

3, 3, 5, 3, 5, 3, 5, 7, 3, 7, 5, 3, 5, 7, 7, 3, 7, 5, 3, 7, 5, 7, 19, 5, 3, 5, 3, 5, 19, 5, 7, 3, 11, 3, 7, 7, 5, 7, 7, 3, 11, 3, 5, 3, 13, 13, 5, 3, 5, 7, 3, 11, 7, 7, 7, 3, 7, 5, 3, 11, 31, 5, 3, 5, 19, 7, 11, 3, 5, 7, 19, 7, 7, 5, 7, 19, 5, 13, 11, 3, 11, 3

Offset

3,1

Comments

If Goldbach's conjecture is true, this sequence is defined for all n.

Links

Table of n, a(n) for n=3..84.

Example

For n = 3, prime(3) = 5, and a(3) = 3 because 5 + 1 - 3 = 3 is prime;
For n = 4, prime(4) = 7, and a(4) = 3 because 7 + 1 - 3 = 5 is prime;
...
for n = 25, prime(n) = 97, and a(n) = 19 because 97 + 1 - 19 = 79 is prime.

Mathematica

f[n_] := Block[{i = 2, p = Prime[n + 2]},
  While[q = Prime[i]; ! PrimeQ[p + 1 - q], i++]; q]; Array[f, 60]

Prog

(PARI) a(n) = my(p=prime(n), q=2); while (!isprime(p+1-q), q = nextprime(q+1)); q; \\ Michel Marcus, Apr 01 2020

Crossrefs

Differs from A119912 after 23 terms.

Sequence in context: A216199 A073081 A094928 * A065507 A182731 A267518

Adjacent sequences: A178981 A178982 A178983 * A178985 A178986 A178987

Keyword

nonn,easy

Author

Lei Zhou, Jan 06 2011

Extensions

More terms from Michel Marcus, Apr 01 2020

Status

approved