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Define an increasing sequence as follows. Start with an initial term, the seed (which need not have the property of the sequence); subsequent terms are obtained by inserting/placing at least one digit in the previous term to obtain the smallest number with the given property. This is the prime sequence with the seed a(1) = 9.
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%I #19 Aug 01 2022 18:24:23

%S 9,19,109,1009,10009,100019,1000159,10001569,100001569,1000015069,

%T 10000135069,100001350649,1000013500649,10000130500649,

%U 100001303500649,1000013032500649,10000103032500649,100001030325003649,1000010130325003649,10000101303250036493

%N Define an increasing sequence as follows. Start with an initial term, the seed (which need not have the property of the sequence); subsequent terms are obtained by inserting/placing at least one digit in the previous term to obtain the smallest number with the given property. This is the prime sequence with the seed a(1) = 9.

%H Alois P. Heinz, <a href="/A068174/b068174.txt">Table of n, a(n) for n = 1..300</a>

%e The primes obtained by inserting/placing a digit in a(2) = 19 are 109, 139, 149, 179, 199 etc. and a(3) = 109 is the smallest.

%t f[n_] := Block[{b = PadLeft[ IntegerDigits[n], Floor[ Log[10, n] + 1]], k = 0}, While[ !PrimeQ[ FromDigits[ Insert[b, k, -2]]], k++ ]; FromDigits[ Insert[b, k, -2]]]; NestList[ f, 9, 18]

%Y Cf. A068166, A068167, A068169, A068170, A068171, A068172, A068173.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Feb 25 2002

%E Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, May 08 2002

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