A109378 Semiprimes at Levenshtein distance n from previous value when considered as a decimal string.

4, 6, 10, 221, 1003, 22226, 100001, 2222245, 10000001, 222222223, 1000000006, 2222222227, 100000000013, 2222222222249, 10000000000015, 222222222222223, 10000000000000031, 22222222222222229, 100000000000000015

Offset

0,1

Comments

For positive n, the string length of a(n+1) is always the 1 + the string length of a(n). This sequence is infinite.

Links

Table of n, a(n) for n=0..18.

Michael Gilleland, Levenshtein Distance, in Three Flavors. [It has been suggested that this algorithm gives incorrect results sometimes. - N. J. A. Sloane]

V. I. Levenshtein, Efficient reconstruction of sequences from their subsequences or supersequences, J. Combin. Theory Ser. A 93 (2001), no. 2, 310-332.

Example

a(0) = 4 = 2^2.
a(1) = 6 because we transform a(0) = 4 to 6 = 2 * 3 (a semiprime) with one substitution.
a(2) = 10 because we transform a(1) = 6 to 10 = 2 * 5 with one substitution and one insertion.
a(3) = 221 because we transform a(2) = 10 to the least semiprime 221 = 13 * 17 with 1 substitution plus two insertion.
a(4) = 1003 because we transform a(3) = 221 to the least semiprime 1003 = 17 * 59 with 3 substitutions plus one insertion and any smaller semiprime can be transformed from 221 in fewer than 4 steps.
a(20) = 10000000000000000001 = 11 * 909090909090909091, which is the least semiprime of Levenshtein distance 20 from a(19) = 2222222222222222222 from which decimal string we transform to a(20) with 19 substitutions and one insertion.

Crossrefs

Cf. A001358, A081355, A081356, A081230, A109809, A109811.

Sequence in context: A234276 A274991 A356755 * A132149 A129235 A012903

Adjacent sequences: A109375 A109376 A109377 * A109379 A109380 A109381

Keyword

easy,nonn,base

Author

Jonathan Vos Post, Aug 25 2005

Status

approved