A178928 Smallest semiprime containing leading sequence of n ascending numbers.

10, 121, 123, 1234, 123451, 1234561, 1234567, 123456782, 12345678911, 123456789101, 123456789101117, 12345678910111229, 123456789101112133, 123456789101112131414, 1234567891011121314159

Offset

1,1

Comments

This is to semiprimes A001358 as A053546 is to primes A000040.

Links

Table of n, a(n) for n=1..15.

Example

a(1) = 10 because 10 = 2 * 5 is the smallest semiprime (or biprime, products of two primes) whose leftmost (base 10) digit is 1.
a(2) = 121 because 121 = 11^2 semiprime whose leftmost digits are 12.
a(3) = 123 since it is a semiprime already.
a(4) = 1234 = 2 * 617.
a(5) = 123451 = 41 * 3011.
a(6) = 1234561 = 211 * 5851.

Mathematica

semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Block[{k = 0, m = FromDigits@ Flatten@ IntegerDigits@ Range@ n}, If[ semiPrimeQ@ m, , While[a = 10^(1 + Max[0, Floor@ Log10@ k]) m + k; ! semiPrimeQ@ a, k++]; m = a]; m]; Array[f, 15]

Crossrefs

Cf. A001358, A053546, A100959.

Sequence in context: A138496 A111482 A095870 * A111695 A027770 A330847

Adjacent sequences: A178925 A178926 A178927 * A178929 A178930 A178931

Keyword

nonn,easy

Author

Jonathan Vos Post, Dec 30 2010

Status

approved