%I #29 Dec 30 2023 23:49:05

%S 1,11,211,4211,34211,234211,4234211,154234211,3154234211,93154234211,

%T 2093154234211,42093154234211,342093154234211,11342093154234211,

%U 3111342093154234211,63111342093154234211,2463111342093154234211,232463111342093154234211

%N a(n+1) is the smallest prime ending with a(n), where a(1)=1.

%H <a href="/A053582/b053582.txt">Table of n, a(n) for n = 1..501</a>

%e The least prime ending with seed 1 is 11; the least prime ending with 11 is 211; the least prime ending with 211 is 4211. - _Clark Kimberling_, Sep 17 2015

%p R:= 1: v:= 1:

%p for iter from 1 to 30 do

%p d:= ilog10(v)+1;

%p for x from v+10^d by 10^d do

%p if isprime(x) then R:= R, x; v:= x; break fi

%p od

%p od:

%p R; # _Robert Israel_, Sep 24 2020

%t f[n_] := f[n] = Block[{j = f[n - 1], k = 1, l = Floor[Log[10, f[n - 1]] + 1]}, While[m = k*10^l + j; ! PrimeQ@ m, k++ ]; m]; f[1] = 1; Array[f, 17]

%t nxt[n_]:=Module[{k=1,p=10^IntegerLength[n]},While[!PrimeQ[k*p+n],k++];k*p+n]; NestList[nxt,1,20] (* _Harvey P. Dale_, Jul 14 2016 *)

%o (Python)

%o from sympy import isprime

%o from itertools import count, islice

%o def agen(an=1): # generator of terms

%o while True:

%o yield an

%o pow10 = 10**len(str(an))

%o for t in count(pow10+an, step=pow10):

%o if isprime(t):

%o an = t

%o break

%o print(list(islice(agen(), 18))) # _Michael S. Branicky_, Jun 23 2022

%Y Cf. A053583, A053584, A069612.

%K base,nonn

%O 1,2

%A _G. L. Honaker, Jr._, Jan 18 2000

%E a(14)-a(17) corrected by _Robert G. Wilson v_, Dec 07 2010