A187885 Numbers n such that n*p + 1 is a square for some prime p.

1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 21, 24, 25, 27, 29, 31, 32, 33, 35, 39, 40, 41, 43, 45, 48, 49, 51, 55, 56, 57, 59, 60, 61, 63, 64, 65, 69, 71, 72, 73, 75, 77, 80, 81, 84, 85, 87, 88, 91, 93, 95, 96, 99, 101, 103, 104, 105, 107, 109, 111, 112, 115, 120

Offset

1,2

Comments

The smallest corresponding p are {3, 5, 2, 3, 5, 3, 7, 13, 2, 11, 13, 3, 19, 17, 3, 2, 23, 29, 31, 29, 7, 3, 37,...}

Links

Table of n, a(n) for n=1..67.

Formula

Complement of A187884.

Example

21 is in the sequence because 21*3 + 1 = 8^2, with p = 3.

Maple

with(numtheory): for k from 1 to 120 do : q:=0:for p from 1 to 200 do : x:=sqrt(k*p+1)
  : if x=trunc(x) and type(p, prime)=true and q=0 then q:=1: printf(`%d, `, k):else
  fi:od:od:

Crossrefs

Cf. A187884, A187886.

Sequence in context: A348004 A260003 A005848 * A039065 A247786 A330565

Adjacent sequences: A187882 A187883 A187884 * A187886 A187887 A187888

Keyword

nonn

Author

Michel Lagneau, Mar 15 2011

Status

approved