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A232129 Largest prime that can be obtained from n by successively appending digits to the right with the constraint that each of the numbers obtained that way must be prime; a(n)=0 if there is no such prime at all.

%I A232129 #17 Nov 04 2024 02:42:09
%S A232129 1979339339,29399999,37337999,4391339,59393339,6733997,73939133,839,
%T A232129 9719,103997939939,113,12791333,13999133,149399,15797,1637,17333,
%U A232129 1811993,1979339339,0,21139,2273993,23399339,24179399,2579939,2699393,27191939,2837,29399999,3079,31379,0,331999799,3491333,35393999
%N A232129 Largest prime that can be obtained from n by successively appending digits to the right with the constraint that each of the numbers obtained that way must be prime; a(n)=0 if there is no such prime at all.
%C A232129 See A232128 for the number of steps required to reach a(n), equal to the length of a(n) minus the length of n. See A232126 for a variant "working backwards", where truncation is considered.
%H A232129 Michael S. Branicky, <a href="/A232129/b232129.txt">Table of n, a(n) for n = 1..10000</a>
%H A232129 Archimedes' Lab, <a href="http://www.archimedes-lab.org/numbers/Num24_69.html">What's Special About This Number?</a>, section about 43.
%e A232129 Starting with 8, one can get the primes 83 and 89 which is larger, but 83 allows one further extension to 839 while 89 does not (no prime in the range 890..899). No further extension is possible, since there are no primes in the range 8390,...,8399. Therefore a(8)=839 and A232128(8)=2.
%e A232129 a(20)=a(42)=0 since no prime can be obtained by appending one digit to 20 or 42.
%o A232129 (PARI) {A232129(n)=local(t(p)=my(m,r=[0,p]);forstep(d=1,9,2,isprime(p*10+d)&&(m=t(10*p+d)+[1,0])[1]>=r[1]&&r=m);r);n<(n=t(n))[2]&&return(n[2])}
%o A232129 (Python)
%o A232129 from sympy import isprime, nextprime
%o A232129 def a(n):
%o A232129     while True:
%o A232129         extends, reach, maxp = -1, {n}, 0
%o A232129         while len(reach) > 0:
%o A232129             candidates = (int(str(e)+d) for d in "1379" for e in reach)
%o A232129             reach1 = set(filter(isprime, candidates))
%o A232129             extends, reach, maxp = extends+1, reach1, max({maxp}|reach1)
%o A232129         return maxp
%o A232129 print([a(n) for n in range(1, 36)]) # _Michael S. Branicky_, Sep 07 2021
%Y A232129 Cf. A232128, A232127, A232126, A232125.
%K A232129 nonn,base
%O A232129 1,1
%A A232129 _M. F. Hasler_, Nov 19 2013