A227509 a(n) = difference between the 2 smallest prime numbers > 10^n.

2, 2, 4, 2, 16, 30, 60, 30, 2, 14, 16, 22, 14, 36, 54, 8, 10, 6, 36, 90, 76, 48, 40, 42, 210, 56, 176, 126, 60, 42, 24, 204, 188, 36, 34, 56, 20, 38, 34, 18, 170, 106, 22, 26, 112, 416, 160, 24, 60, 296, 126, 64, 30, 126, 136, 6, 84, 10, 174, 60, 286, 126, 186, 6

Offset

1,1

Comments

(Sum_{n=1..N} a(n)/n)/N appears to tend to log(10) as N increases.

Links

Pierre CAMI, Table of n, a(n) for n = 1..1825

Example

10^1+1=11 is prime as is 13 so a(1)=2.
10^2+1=101 is prime as is 103 so a(2)=2.

Mathematica

spn[n_]:=Module[{a=NextPrime[10^n]}, NextPrime[a]-a]; Array[spn, 70] (* Harvey P. Dale, Sep 01 2017 *)

Prog

PFGW & SCRIPT
SCRIPT
DIM n, 0
DIM k
DIM g
DIMS t
OPENFILEOUT myfile, a(n).txt
LABEL a
SET n, n+1
SET k, -1
LABEL b
SET k, k+2
SETS t, %d, %d\,; n; k
PRP 10^n+k, t
IF ISPRP THEN GOTO c
GOTO b
LABEL c
SET g, k
LABEL d
SET k, k+2
SETS t, %d, %d\,; n; k
PRP 10^n+k, t
IF ISPRP THEN GOTO e
GOTO d
LABEL e
SET g, k-g
SETS t, %d, %d, %d\,; n; g; k
WRITE myfile, t
GOTO a

Crossrefs

Sequence in context: A359442 A102416 A333595 * A279094 A299148 A129243

Adjacent sequences: A227506 A227507 A227508 * A227510 A227511 A227512

Keyword

nonn

Author

Pierre CAMI, Jul 14 2013

Status

approved