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

Author

Amarnath Murthy, Feb 25 2002

Keywords

• base
• nonn

Comments

a(5) onwards the sequence is A068166.

Examples

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

Links

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

Crossrefs

Cf. A068166, A068167.

Programs

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

Extensions

Corrected and extended by Robert Gerbicz, Sep 06 2002