%I #4 Mar 30 2012 17:28:20
%S 101,1013,1019,1021,1031,1033,1039,1049,1069,1091,1093,1097,1109,1129,
%T 1193,1213,1217,1231,1237,1277,1279,1289,1291,1297,1327,1367,1373,
%U 1433,1439,1453,1459,1489,1493,1499,1549,1559,1579,1597,1657,1667,1669,1693
%N Slowest increasing sequence of primes such that two neighbor terms share at least three digits (counted with multiplicity).
%C Presumably contains almost all primes.
%C Sequences for other seeds (they are shortened when they converge with the first sequence):
%C {101,1013,1019,1021,1031,1033,1039,1049,1069,1091,1093,1097,1109,1129,1193,1213,1217,1231,1237,
%C 1277,1279,1289,1291,1297,1327,1367,1373,1433,1439,1453,1459,1489,1493,1499,1549,1559,1579},
%C {103,1013},
%C {107,701,1087,1097,1109,1129,1193},
%C {109,1009,1019},
%C {113,131,311,1013,1019},
%C {127,271,1217},
%C {131,311,1013,1019},
%C {137,173,317,1237},
%C {139,193,1039},
%C {149,419,491,941,1049},
%C {151,1051,1061,1063,1069},
%C {157,571,751,1567,1571,1579},
%C {163,613,631,1063,1069},
%C {167,617,761,1367},
%C {173,317,1237}.
%C Conjecture: for any initial seed, sequence eventually merges with the first one.
%o (PARI) common(a,b)={my(aa=vecsort(eval(Vec(Str(a)))),bb=vecsort(eval(Vec(Str(b)))),i=1,j=1,t=0);while(i<=#aa&&j<=#bb,if(aa[i]==bb[j],t++;i++;j++,if(aa[i]>bb[j],j++,i++)));t};q=101;n=1;print1(q);forprime(p=997,1e4,if(common(p,q)>2,print1(","p);q=p))
%Y Cf. A133835.
%K nonn,base,easy
%O 1,1
%A _Zak Seidov_, Sep 26 2007
%E Program and comment by _Charles R Greathouse IV_, Sep 11 2009