A133835 Slowest increasing sequence of primes such that two neighbor terms share at least two digits (counted with multiplicity).

11, 101, 103, 107, 109, 139, 149, 179, 191, 193, 197, 199, 419, 421, 431, 433, 439, 443, 449, 479, 487, 547, 557, 571, 577, 587, 751, 757, 773, 787, 797, 877, 887, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..49.

Mathematica

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}]

Crossrefs

Sequence in context: A330291 A318647 A185121 * A326108 A292451 A292731

Adjacent sequences: A133832 A133833 A133834 * A133836 A133837 A133838

Keyword

nonn,base

Author

Zak Seidov, Sep 26 2007

Status

approved