1,1

Sequences for other seeds:

{11,101,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},

{13,31,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},

{17,71,107,109,139,149,179,191,193,197,199,419,421,431,433,439},

{19,109,139,149,179,191,193,197,199,419,421,431,433,439},

{23,223,227,229,239,263,269,293,349,359,379,389,397,439},

{29,229,239,263,269,293,349,359,379,389,397,439},

{31,103,107,109,139,149,179,191,193,197,199,419,421,431,433,439},

{37,73,137,139,149,179,191,193,197,199,419,421,431,433,439},

{41,149,179,191,193,197,199,419,421,431,433,439},

{43,347,349,359,379,389,397,439},

{47,347,349,359,379,389,397,439},

{53,353,359,379,389,397,439},

{59,359,379,389,397,439},

{61,163,167,173,179,191,193,197,199,419,421,431,433,439},

{67,167,173,179,191,193,197,199,419,421,431,433,439},

{71,107,109,139,149,179,191,193,197,199,419,421,431,433,439}.

Conjecture: for any initial seed, sequence eventually merges with the first one.

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}]

Sequence in context: A127806 A036929 A073053 this_sequence A043494 A038444 A115824

Adjacent sequences: A133832 A133833 A133834 this_sequence A133836 A133837 A133838

nonn,base

Zak Seidov (zakseidov(AT)yahoo.com), Sep 26 2007