A034276 - OEIS

%I #25 Nov 05 2025 15:21:55

%S 11,29,2,5,41,251,43,145577,51941,4372877,26901631,366636187,

%T 15387286403,218761753811,3313980408469

%N Smallest prime that generates a prime pyramid of height n.

%C Let p be prime; look for the smallest prime in {1|p|1, 3|p|3, 7|p|7, 9|p|9}, where '|' stands for concatenation; repeat until no such prime can be found; then height(p) = number of rows in pyramid.

%C a(13) > 10^10. - _Donovan Johnson_, Aug 13 2010

%H H. Heinz, Patterns in Primes, <a href="http://www.magic-squares.net/primes.htm">Illustrating Two Prime Pyramids</a>

%H Chai Wah Wu, <a href="https://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 Example for p=43: 43 3433 334333 93343339 3933433393 939334333939 39393343339393, stop; height(43)=7.

%Y Cf. A047076, A053600, A052205, A256957, A052091, A052092.

%K nonn,nice,base,more

%O 1,1

%A _Felice Russo_, Jan 25 2000

%E More terms from _Naohiro Nomoto_, Jul 14 2001

%E a(11)-a(12) from _Donovan Johnson_, Aug 13 2010

%E a(13) from _Chai Wah Wu_, Apr 10 2015

%E a(14)-a(15) from _Giovanni Resta_, May 15 2020