A246826 Numbers n such that there is no prime of a prime twin pair between n^2 + n and n^2 + 3*n + 2.

0, 10, 26, 30, 36, 136, 156, 433

Offset

1,2

Comments

No more values for n = 434 to 45140.

Conjecture: the sequence is finite and given in full.

a(9), if it exists, is greater than 10^5. - Derek Orr, Sep 19 2014

Links

Table of n, a(n) for n=1..8.

Example

n = 0 only 1 between 0 and 2 so a(1) = 0.
n = 1 between 2 and 6, 3 is the first of twin pair 3, 5.
For n = 2 to 9 always at least one prime of a twin pair between n^2 + n and n^2 + 3*n + 2.
n = 10 no prime of a twin pair between 110 and 132 so a(2) = 10.

Prog

(PARI)
a(n)=forprime(p=n^2+n, n^2+3*n+2, if(precprime(p-1)==p-2||nextprime(p+1)==p+2, return(0))); return(1)
n=0; while(n<10^5, if(a(n), print1(n, ", ")); n++) \\ Derek Orr, Sep 19 2014

Crossrefs

Cf. A091592, A108309.

Sequence in context: A259297 A358774 A046961 * A125035 A337049 A067264

Adjacent sequences: A246823 A246824 A246825 * A246827 A246828 A246829

Keyword

nonn

Author

Pierre CAMI, Sep 04 2014

Status

approved