A120729 Smallest integer k>0 such that k*10^n + 1 is a semiprime.

3, 2, 2, 5, 1, 1, 1, 1, 1, 2, 4, 2, 3, 7, 4, 3, 6, 6, 4, 1, 2, 4, 13, 2, 4, 3, 7, 21, 6, 9, 3, 1, 5, 4, 16, 19, 28, 19, 9, 3

Offset

0,1

Comments

The corresponding semiprimes are 4, 21, 201, 5001, 10001, 100001, 100001, 10000001, 2000000001, 40000000001, ... Semiprime analog of A121172.

Links

Table of n, a(n) for n=0..39.

Formula

Smallest integer k>0 such that k*10^n + 1 is in A001358.

Example

a(0) = 3 because 3*10^0 + 1 = 4 = 2^2 is a semiprime.
a(1) = 2 because 2*10^1 + 1 = 21 = 3*7 is a semiprime.
a(2) = 2 because 2*10^2 + 1 = 201 = 3*67 is a semiprime.
a(3) = 5 because 5*10^3 + 1 = 5001 = 3*1667 is a semiprime.
a(4) = 1 because 1*10^4 + 1 = 10001 = 73*137 is a semiprime.
a(5) = 1 because 1*10^5 + 1 = 100001 = 11*9091 is a semiprime.

Mathematica

sik[n_]:=Module[{k=1, c=10^n}, While[PrimeOmega[k*c+1]!=2, k++]; k]; Array[sik, 40, 0] (* Harvey P. Dale, Aug 20 2012 *)

Crossrefs

Cf. A001358, A030430, A037071, A062800, A065582, A121172.

Sequence in context: A247501 A192183 A133518 * A205139 A092743 A139420

Adjacent sequences: A120726 A120727 A120728 * A120730 A120731 A120732

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 17 2006

Extensions

More terms from Harvey P. Dale, Aug 20 2012

Status

approved