A331566 Smallest prime p such that p*A014574(n) is adjacent to a prime.

2, 2, 2, 2, 2, 2, 3, 5, 3, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 5, 3, 3, 2, 2, 2, 2, 2, 3, 2, 5, 3, 2, 2, 2, 3, 7, 3, 2, 2, 2, 3, 5, 2, 2, 2, 3, 2, 3, 3, 7, 3, 5, 7, 5, 2, 3, 11, 2, 3, 2, 3, 2, 2, 7, 3, 2, 2, 5, 2, 5, 5, 5, 11, 3, 2, 5, 2, 3, 5, 2, 11, 7, 2, 2, 2, 7, 2, 11

Offset

1,1

Comments

For A014574(n) < 1000000, the largest value of a(n) is 79 and 30.6% of all a(n) are 2.

Links

Table of n, a(n) for n=1..92.

Example

a(1) = 2, because 2*4 = 8 is adjacent to prime 7.
a(2) = 2, because 2*6 = 12 is adjacent to prime 11.
a(3) = 2, because 2*12 = 24 is adjacent to prime 23.
a(4) = 2, because 2*18 = 36 is adjacent to prime 37.
a(5) = 2, because 2*30 = 60 is adjacent to prime 59.
a(10) = 5, because 5*108 = 540 is adjacent to prime 541.

Mathematica

twinMids = Select[Range[3500], And @@ PrimeQ[# + {-1, 1}] &]; leastPrime[n_] := Module[{p = 2}, While[!Or @@ PrimeQ[p * n + {-1, 1}], p = NextPrime[p]]; p]; leastPrime /@ twinMids (* Amiram Eldar, Jan 21 2020 *)

Crossrefs

Cf. A014574.

Sequence in context: A035665 A352829 A307833 * A358473 A369978 A083261

Adjacent sequences: A331563 A331564 A331565 * A331567 A331568 A331569

Keyword

nonn

Author

Dmitry Kamenetsky, Jan 20 2020

Status

approved