|
%I #2 Mar 30 2012 17:26:23
%S 11,101,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439,
%T 443,449,479,487,547,557,571,577,587,751,757,773,787,797,877,887,1087,
%U 1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193
%N Slowest increasing sequence of primes such that two neighbor terms share at least two digits (counted with multiplicity).
%C Sequences for other seeds:
%C {11,101,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C {13,31,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C {17,71,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C {19,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C {23,223,227,229,239,263,269,293,349,359,379,389,397,439},
%C {29,229,239,263,269,293,349,359,379,389,397,439},
%C {31,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C {37,73,137,139,149,179,191,193,197,199,419,421,431,433,439},
%C {41,149,179,191,193,197,199,419,421,431,433,439},
%C {43,347,349,359,379,389,397,439},
%C {47,347,349,359,379,389,397,439},
%C {53,353,359,379,389,397,439},
%C {59,359,379,389,397,439},
%C {61,163,167,173,179,191,193,197,199,419,421,431,433,439},
%C {67,167,173,179,191,193,197,199,419,421,431,433,439},
%C {71,107,109,139,149,179,191,193,197,199,419,421,431,433,439}.
%C Conjecture: for any initial seed, sequence eventually merges with the first one.
%t MultiIntersection[l1_List, l2_List]:=Module[{nl, f}, f[x_]:={First[ # ], Length[ # ]}&/@Split[Sort[x]]; nl=Sort[Join[Flatten[Map[f, {l1, l2}], 1]]]; nl=Split[nl, #[[1]]===#2[[1]]&]; Flatten[Cases[nl, {{x_, m_}, {x_, n_}} :-> Table[x, {m}]], 1]] f:=(a=Prime[k]; ida=IntegerDigits[a]; c=1; s[1]=a; Do[p=Prime[i]; If[Length[MultiIntersection[ida, IntegerDigits[p]]]>1, c++; s[c]=p; a=p; ida=IntegerDigits[a]], {i, k+1, 100}]; s[ # ]&/@Range[c]); Table[f, {k, 5, 20}]
%K nonn,base
%O 1,1
%A _Zak Seidov_, Sep 26 2007
|
