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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.
12
2, 23, 223, 1223, 10223, 102023, 1020023, 10200263, 102002603, 1020026303, 10200226303, 102002263031, 1020002263031, 10200022363031, 102000223263031, 1020000223263031, 10200002232630131, 102000022326301313, 1020000222326301313, 10200002223236301313
OFFSET
1,1
LINKS
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
Sequence in context: A288820 A340296 A242904 * A030456 A357436 A069837
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Feb 25 2002
EXTENSIONS
Corrected and extended by Robert Gerbicz, Sep 06 2002
STATUS
approved