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A133835 Slowest increasing sequence of primes such that two neighbor terms share at least two digits (counted with multiplicity). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A168586 A318647 A185121 * A326108 A292451 A292731

Adjacent sequences:  A133832 A133833 A133834 * A133836 A133837 A133838

KEYWORD

nonn,base

AUTHOR

Zak Seidov, Sep 26 2007

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)