A131194 Slowest increasing sequence of primes such that two neighbor terms share at least three digits (counted with multiplicity).

101, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1069, 1091, 1093, 1097, 1109, 1129, 1193, 1213, 1217, 1231, 1237, 1277, 1279, 1289, 1291, 1297, 1327, 1367, 1373, 1433, 1439, 1453, 1459, 1489, 1493, 1499, 1549, 1559, 1579, 1597, 1657, 1667, 1669, 1693

Offset

1,1

Comments

Presumably contains almost all primes.

Sequences for other seeds (they are shortened when they converge with the first sequence):

{101,1013,1019,1021,1031,1033,1039,1049,1069,1091,1093,1097,1109,1129,1193,1213,1217,1231,1237,

1277,1279,1289,1291,1297,1327,1367,1373,1433,1439,1453,1459,1489,1493,1499,1549,1559,1579},

{103,1013},

{107,701,1087,1097,1109,1129,1193},

{109,1009,1019},

{113,131,311,1013,1019},

{127,271,1217},

{131,311,1013,1019},

{137,173,317,1237},

{139,193,1039},

{149,419,491,941,1049},

{151,1051,1061,1063,1069},

{157,571,751,1567,1571,1579},

{163,613,631,1063,1069},

{167,617,761,1367},

{173,317,1237}.

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

Links

Table of n, a(n) for n=1..42.

Prog

(PARI) common(a, b)={my(aa=vecsort(eval(Vec(Str(a)))), bb=vecsort(eval(Vec(Str(b)))), i=1, j=1, t=0); while(i<=#aa&&j<=#bb, if(aa[i]==bb[j], t++; i++; j++, if(aa[i]>bb[j], j++, i++))); t}; q=101; n=1; print1(q); forprime(p=997, 1e4, if(common(p, q)>2, print1(", "p); q=p))

Crossrefs

Cf. A133835.

Sequence in context: A171823 A289528 A289771 * A124015 A099182 A048177

Adjacent sequences: A131191 A131192 A131193 * A131195 A131196 A131197

Keyword

nonn,base,easy

Author

Zak Seidov, Sep 26 2007

Extensions

Program and comment by Charles R Greathouse IV, Sep 11 2009

Status

approved