A124001 Difference between first twin prime > 10^n and 10^n.

2, 1, 1, 19, 7, 151, 37, 139, 37, 7, 277, 817, 61, 1267, 97, 2371, 1549, 19, 619, 97, 391, 409, 649, 5527, 2731, 559, 949, 427, 601, 2797, 1681, 7189, 2449, 6751, 7597, 8419, 16879, 871, 5569, 10327, 16111, 2131, 6121, 23329, 5179, 4249, 2641, 2257, 3997

Offset: 0

Author

Zak Seidov, Nov 01 2006

Keywords

• nonn

Comments

a(n) >= A033873(n) and a(n) = A033873(n) for n = 1, 2, 4, 9.

As N increases, the ratio (Sum_{n=1..N} a(n)/n^2)/N tends to 4. - Pierre CAMI, Jul 12 2013

Examples

			a(0) = 2 because 3 and 5 are twin primes and 3 - 10^0 = 2,
a(1) = 1 because 11 and 13 are twin primes and 11 - 10^1 = 1,
a(2) = 1 because 101 and 103 are twin primes and 101 - 10^2 = 1,
a(3) = 19 because 1019 and 1021 are twin primes and 1019 - 10^3 = 19, etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..1250 (first 476 terms from _Pierre CAMI_).

Crossrefs

Cf. A033873, A092245.

Programs

Mathematica

f[n_] := Block[{p = q = NextPrime[10^n]}, While[p + 2 != q, p = q; q = NextPrime@ q]; p - 10^n]; Array[f, 49, 0] (* Robert G. Wilson v, Nov 28 2015 *)
ftp[n_]:=Module[{p=NextPrime[n]},While[CompositeQ[p+2],p=NextPrime[p]];p-n]; Table[ftp[10^n],{n,0,50}] (* Harvey P. Dale, Oct 15 2019 *)

Formula

a(n) = A092245(n+1) - 10^n. - Robert G. Wilson v, Nov 28 2015