cp's OEIS Frontend

A256957 Smallest palindromic prime that generates a palindromic prime pyramid of height n.

%I A256957 #18 Oct 28 2024 15:45:14
%S A256957 11,131,2,5,10301,16361,10281118201,35605550653,7159123219517,
%T A256957 17401539893510471,3205657651567565023,14736384418081448363741
%N A256957 Smallest palindromic prime that generates a palindromic prime pyramid of height n.
%C A256957 Start with a palindromic prime p; look for smallest palindromic prime that has previous term as a centered substring and has 2 more digits (i.e., one more digit at each end); repeat until no such palindromic prime can be found; then height(p) = number of rows in pyramid. Each row of pyramid must be the smallest prime that can be used. Then a(n) = smallest value of p that generates a pyramid of height n.
%H A256957 G. L. Honaker, Jr. and Chris K. Caldwell, <a href="http://www.utm.edu/staff/caldwell/preprints/jrm_prime_pyramids.pdf">Palindromic prime pyramids</a>
%H A256957 Ivars Peterson's MathTrek, <a href="https://www.sciencenews.org/article/primes-palindromes-and-pyramids">Primes, Palindromes, and Pyramids</a>
%H A256957 Chai Wah Wu, <a href="http://arxiv.org/abs/1503.08883">On a conjecture regarding primality of numbers constructed from prepending and appending identical digits</a>, arXiv:1503.08883 [math.NT], 2015.
%e A256957 a(1) = 11.
%e A256957 a(4) = 5:
%e A256957 5
%e A256957 151
%e A256957 31513
%e A256957 3315133, stop;
%e A256957 height(5)=4.
%e A256957 a(6)=16362:
%e A256957 16361
%e A256957 1163611
%e A256957 311636113
%e A256957 33116361133
%e A256957 3331163611333
%e A256957 333311636113333, stop;
%e A256957 height(16361)=6.
%Y A256957 Cf. A034276, A052205, A053600.
%K A256957 nonn,base,more
%O A256957 1,1
%A A256957 _Felice Russo_, Jan 25 2000
%E A256957 Added a(10)-a(11) and corrected a(4) -  _Chai Wah Wu_, Apr 09 2015
%E A256957 Entry revised by _N. J. A. Sloane_, Apr 13 2015
%E A256957 a(12) from _Michael S. Branicky_, Oct 28 2024