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A052091 Left parts needed for the construction of the palindromic prime pyramid starting with 2.

%I A052091 #18 Aug 11 2024 14:41:32
%S A052091 2,7,3,33,9,30,18,92,3,133,18,117,17,15,346,93,33,180,120,194,126,336,
%T A052091 331,330,95,12,118,369,39,32,165,313,165,134,13,149,195,145,158,720,
%U A052091 18,396,193,102,737,964,722,156,106,395,945,303,310,113,150,303,715,123
%N A052091 Left parts needed for the construction of the palindromic prime pyramid starting with 2.
%C A052091 Each term is the smallest to have the previous term as a centered substring, beginning with the smallest palindromic prime 2. The right parts are the reversals of the above terms leading zeros included. The terms from a(34) onward currently correspond only to strong pseudoprimes.
%C A052091 For n > 0, the leftmost (most significant) digit of a(n) is either 1, 3, 7 or 9. - _Chai Wah Wu_, Dec 02 2015
%H A052091 Chai Wah Wu, <a href="/A052091/b052091.txt">Table of n, a(n) for n = 0..501</a>
%H A052091 P. De Geest, <a href="https://www.worldofnumbers.com/palprim3.htm">World!Of Palindromic Primes, Page 3</a>
%e A052091 Start with 2; add 7 gives 727; add 3 gives 37273; add 33 gives 333727333; etc.
%o A052091 (Python)
%o A052091 from sympy import isprime
%o A052091 A052091_list, p = [2], 2
%o A052091 for _ in range(30):
%o A052091     m, ps = 1, str(p)
%o A052091     s = int('1'+ps+'1')
%o A052091     while not isprime(s):
%o A052091         m += 1
%o A052091         ms = str(m)
%o A052091         if ms[0] in '268':
%o A052091             ms = str(int(ms[0])+1) + '0'*(len(ms)-1)
%o A052091             m = int(ms)
%o A052091         if ms[0] in '45':
%o A052091             ms = '7' + '0'*(len(ms)-1)
%o A052091             m = int(ms)
%o A052091         s = int(ms+ps+ms[::-1])
%o A052091     p = s
%o A052091     A052091_list.append(m) # _Chai Wah Wu_, Dec 02 2015
%Y A052091 Cf. A053600, A052092, A047076.
%K A052091 nonn,base
%O A052091 0,1
%A A052091 _Patrick De Geest_, Jan 15 2000
%E A052091 Comments from _G. L. Honaker, Jr._, Mar 30 2000