A177688 Numbers n such that (n+2)//n - (n+1) is prime, where // represents the concatenation of decimals.

0, 1, 4, 6, 7, 9, 12, 13, 15, 18, 19, 22, 25, 28, 31, 33, 39, 46, 48, 49, 52, 60, 61, 64, 67, 73, 75, 84, 85, 88, 90, 99, 100, 103, 106, 132, 133, 135, 136, 138, 142, 156, 160, 163, 171, 178, 181, 183, 187, 190, 198, 201, 202, 211, 220, 222, 229, 238, 241, 246, 252

Offset

1,3

Comments

If n is a k-digit number, then we demand that p = (n+2) * 10^k + n - (n+1) is a prime number, obviously of the form p = (n+2) * 10^k - 1, so the decimal representation of p is n+1 followed by k times the digit 9.

The sequence is infinite, proof with Dirichlet's prime number (in arithmetic progressions) theorem.

Note that numbers of the form (n+2)//n + (n+1) are multiples of 3 and do not generate primes.

Links

Table of n, a(n) for n=1..61.

Example

2//0 - 1 = 20 - 1 = 19 = prime(8), 0 is first term;
3//1 - 2 = 31 - 2 = 29 = prime(10), 1 is 2nd term;
6//4 - 5 = 64 - 5 = 59 = prime(17), 4 is 3rd term.

Mathematica

n2ncQ[n_]:=PrimeQ[FromDigits[Join[IntegerDigits[n+2], IntegerDigits[ n]]]- n-1]; Select[Range[0, 300], n2ncQ]  (* Harvey P. Dale, Feb 24 2011 *)

Crossrefs

Cf. A000040, A065582, A095995, A173976, A177435.

Sequence in context: A345665 A343177 A085817 * A190250 A047508 A089960

Adjacent sequences: A177685 A177686 A177687 * A177689 A177690 A177691

Keyword

base,easy,nonn

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 11 2010

Status

approved