A068167 Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 2.

2, 23, 223, 1223, 10223, 102023, 1020023, 10200263, 102002603, 1020026303, 10200226303, 102002263031, 1020002263031, 10200022363031, 102000223263031, 1020000223263031, 10200002232630131, 102000022326301313, 1020000222326301313, 10200002223236301313

Offset

1,1

Links

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

Example

The primes that can be obtained by inserting/placing a digit in a(2) = 23 are 223, 233, 239, 263, 283, 293, etc. a(3) = 223 is the smallest.

Maple

a:= proc(n) option remember; local s, w, m;
      if n=1 then 2
    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, A030456.

Sequence in context: A288820 A340296 A242904 * A030456 A357436 A069837

Adjacent sequences: A068164 A068165 A068166 * A068168 A068169 A068170

Keyword

base,nonn

Author

Amarnath Murthy, Feb 25 2002

Extensions

Corrected and extended by Robert Gerbicz, Sep 06 2002

Status

approved