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A375956 a(0) = 2; for n > 0, a(n) is the smallest palindromic prime containing exactly n more digits on each end than a(n-1), with a(n-1) as the central substring.

%I A375956 #32 Sep 29 2024 13:18:25
%S A375956 2,727,1572751,1081572751801,100210815727518012001,
%T A375956 1001410021081572751801200141001,
%U A375956 1000141001410021081572751801200141001410001,100001610001410014100210815727518012001410014100016100001,1000005310000161000141001410021081572751801200141001410001610000135000001
%N A375956 a(0) = 2; for n > 0, a(n) is the smallest palindromic prime containing exactly n more digits on each end than a(n-1), with a(n-1) as the central substring.
%C A375956 a(32) has 1057 digits. - _Michael S. Branicky_, Sep 29 2024
%H A375956 Michael S. Branicky, <a href="/A375956/b375956.txt">Table of n, a(n) for n = 0..31</a>
%e A375956 a(1) = 727, because 727 is prime and no lesser number verify this property.
%e A375956 As a triangle:
%e A375956                                      2
%e A375956                                     727
%e A375956                                   1572751
%e A375956                                1081572751801
%e A375956                            100210815727518012001
%e A375956                       1001410021081572751801200141001
%e A375956                 1000141001410021081572751801200141001410001
%e A375956          100001610001410014100210815727518012001410014100016100001
%e A375956  1000005310000161000141001410021081572751801200141001410001610000135000001
%o A375956 (Python)
%o A375956 from itertools import count, islice
%o A375956 from sympy import isprime
%o A375956 def A375956_gen(): # generator of terms
%o A375956     a, l, r = 2, 1, 10
%o A375956     yield 2
%o A375956     for n in count(1):
%o A375956         b = 10**n
%o A375956         c = b*r
%o A375956         for i in count(10**(n-1)):
%o A375956             m = c*i+a*b+int(str(i)[::-1])
%o A375956             if isprime(m):
%o A375956                 yield m
%o A375956                 a = m
%o A375956                 l += n<<1
%o A375956                 r *= 10**(n<<1)
%o A375956                 break
%o A375956 A375956_list = list(islice(A375956_gen(),20)) # _Chai Wah Wu_, Sep 27 2024
%Y A375956 Cf. A375690.
%K A375956 nonn,base
%O A375956 0,1
%A A375956 _Jean-Marc Rebert_, Sep 03 2024