Search: id:A133835
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%I A133835
%S A133835 11,101,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439,443,
%T A133835 449,479,487,547,557,571,577,587,751,757,773,787,797,877,887,1087,1091,
%U A133835 1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193
%N A133835 Slowest increasing sequence of primes such that two neighbor terms share 
               at least two digits (counted with multiplicity).
%C A133835 Sequences for other seeds:
%C A133835 {11,101,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {13,31,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {17,71,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {19,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {23,223,227,229,239,263,269,293,349,359,379,389,397,439},
%C A133835 {29,229,239,263,269,293,349,359,379,389,397,439},
%C A133835 {31,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {37,73,137,139,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {41,149,179,191,193,197,199,419,421,431,433,439},
%C A133835 {43,347,349,359,379,389,397,439},
%C A133835 {47,347,349,359,379,389,397,439},
%C A133835 {53,353,359,379,389,397,439},
%C A133835 {59,359,379,389,397,439},
%C A133835 {61,163,167,173,179,191,193,197,199,419,421,431,433,439},
%C A133835 {67,167,173,179,191,193,197,199,419,421,431,433,439},
%C A133835 {71,107,109,139,149,179,191,193,197,199,419,421,431,433,439}.
%C A133835 Conjecture: for any initial seed, sequence eventually merges with the 
               first one.
%t A133835 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}]
%Y A133835 Sequence in context: A127806 A036929 A073053 this_sequence A043494 A038444 
               A115824
%Y A133835 Adjacent sequences: A133832 A133833 A133834 this_sequence A133836 A133837 
               A133838
%K A133835 nonn,base
%O A133835 1,1
%A A133835 Zak Seidov (zakseidov(AT)yahoo.com), Sep 26 2007

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