

A131194


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


0



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
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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



