cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A109378 #13 Dec 01 2018 04:31:14
%S A109378 4,6,10,221,1003,22226,100001,2222245,10000001,222222223,1000000006,
%T A109378 2222222227,100000000013,2222222222249,10000000000015,222222222222223,
%U A109378 10000000000000031,22222222222222229,100000000000000015
%N A109378 Semiprimes at Levenshtein distance n from previous value when considered as a decimal string.
%C A109378 For positive n, the string length of a(n+1) is always the 1 + the string length of a(n). This sequence is infinite.
%H A109378 Michael Gilleland, <a href="https://people.cs.pitt.edu/~kirk/cs1501/Pruhs/Spring2006/assignments/editdistance/Levenshtein%20Distance.htm">Levenshtein Distance, in Three Flavors</a>. [It has been suggested that this algorithm gives incorrect results sometimes. - _N. J. A. Sloane_]
%H A109378 V. I. Levenshtein, <a href="https://doi.org/10.1006/jcta.2000.3081">Efficient reconstruction of sequences from their subsequences or supersequences</a>, J. Combin. Theory Ser. A 93 (2001), no. 2, 310-332.
%e A109378 a(0) = 4 = 2^2.
%e A109378 a(1) = 6 because we transform a(0) = 4 to 6 = 2 * 3 (a semiprime) with one substitution.
%e A109378 a(2) = 10 because we transform a(1) = 6 to 10 = 2 * 5 with one substitution and one insertion.
%e A109378 a(3) = 221 because we transform a(2) = 10 to the least semiprime 221 = 13 * 17 with 1 substitution plus two insertion.
%e A109378 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.
%e A109378 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.
%Y A109378 Cf. A001358, A081355, A081356, A081230, A109809, A109811.
%K A109378 easy,nonn,base
%O A109378 0,1
%A A109378 _Jonathan Vos Post_, Aug 25 2005