A068168 Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 3.

3, 13, 103, 1013, 10103, 100103, 1001003, 10010023, 100010023, 1000100239, 10001000239, 100010002039, 1000100020319, 10001000200319, 100001000200319, 1000010002000319, 10000100002000319, 100001000020003109, 1000010000200031039, 10000100002000310329

Offset

1,1

Comments

a(5) onwards the sequence is A068166.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..300

Example

The primes obtained by inserting/placing a digit in a(2) = 13 are 113,131,313 etc... a(3)= 113 is the smallest.

Maple

a:= proc(n) option remember; local s, w, m;
      if n=1 then 3
    else w:=a(n-1); s:=""||w; m:=length(s);
         min(select(x->length(x)=m+1 and isprime(x),
         {seq(seq(parse(cat(seq(s[h], h=1..i), j,
         seq(s[h], h=i+1..m))), j=0..9), i=0..m)})[])
      fi
    end:
seq(a(n), n=1..23);  # Alois P. Heinz, Nov 07 2014

Crossrefs

Cf. A068166, A068167.

Sequence in context: A352170 A240167 A127004 * A215126 A228148 A098027

Adjacent sequences: A068165 A068166 A068167 * A068169 A068170 A068171

Keyword

base,nonn

Author

Amarnath Murthy, Feb 25 2002

Extensions

Corrected and extended by Robert Gerbicz, Sep 06 2002

Status

approved