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Beginning with 6, numbers such that every partial concatenation has the same prime signature p*q.
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%I #19 Jul 07 2023 15:16:36

%S 6,2,2,7,7,1,1,8,7,3,3,9,1,3,13,3,7,3,11,3,7,3,3,15,9,9,17,3,102,3,22,

%T 7,7,51,3,7,26,43,9,39,8,1,29,7,39,53,7,59,81,39,41,1,11,47,23,39,13,

%U 13,89,15,101,7,17,21,7,3,81,51,23,31,23,1,3,3,39

%N Beginning with 6, numbers such that every partial concatenation has the same prime signature p*q.

%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%e 62, 622, 6227, 62277, etc. have the same prime signature p*q.

%o (PARI) digs(k) = if (k, digits(k), [0]);

%o isok(vd, k) = {newv = concat(vd, digs(k)); val = fromdigits(newv); (bigomega(val) == 2) && (omega(val) == 2);}

%o fnew(vd) = {k = 0; while (! isok(vd, k), k++); k;}

%o lista(nn) = {k = 6; v = [k]; vd = digs(k); print1(v[1], ", "); for (n=2, nn, k = fnew(vd); print1(k, ", "); v = concat(v, k); vd = concat(vd, digs(k)););} \\ _Michel Marcus_, Jan 21 2017

%Y Cf. A006881.

%K nonn,base

%O 1,1

%A _Amarnath Murthy_, Apr 17 2004

%E More terms from _David Wasserman_, Jun 07 2007

%E Edited and a(69)-a(85) moved to comments by _Michel Marcus_, Jan 21 2017

%E More terms from _Jinyuan Wang_, Jul 09 2020