A068167 - OEIS

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.

%I #19 Sep 13 2015 04:59:20

%S 2,23,223,1223,10223,102023,1020023,10200263,102002603,1020026303,

%T 10200226303,102002263031,1020002263031,10200022363031,

%U 102000223263031,1020000223263031,10200002232630131,102000022326301313,1020000222326301313,10200002223236301313

%N 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.

%H Alois P. Heinz, <a href="/A068167/b068167.txt">Table of n, a(n) for n = 1..300</a>

%e 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.

%p a:= proc(n) option remember; local s, w, m;

%p if n=1 then 2

%p else w:=a(n-1); s:=""||w; m:=length(s);

%p min(select(x->length(x)=m+1 and isprime(x),

%p {seq(seq(parse(cat(seq(s[h], h=1..i), j,

%p seq(s[h], h=i+1..m))), j=0..9), i=0..m)})[])

%p fi

%p end:

%p seq(a(n), n=1..23); # _Alois P. Heinz_, Nov 07 2014

%Y Cf. A068166, A030456.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Feb 25 2002

%E Corrected and extended by _Robert Gerbicz_, Sep 06 2002