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

11, 131, 2, 5, 10301, 16361, 10281118201, 35605550653, 7159123219517, 17401539893510471, 3205657651567565023

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..11.

G. L. Honaker, Jr. and Chris K. Caldwell, Palindromic prime pyramids

Ivars Peterson's MathTrek, Primes, Palindromes, and Pyramids

Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.

Example

a(1) = 11.
a(4) = 5:
5
151
31513
3315133, stop;
height(5)=4.
a(6)=16362:
16361
1163611
311636113
33116361133
3331163611333
333311636113333, stop;
height(16361)=6.

Crossrefs

Cf. A034276, A052205, A053600.

Sequence in context: A184280 A266947 A157718 * A046210 A100757 A099677

Adjacent sequences: A256954 A256955 A256956 * A256958 A256959 A256960

Keyword

nonn,base,more

Author

Felice Russo, Jan 25 2000

Extensions

Added a(10)-a(11) and corrected a(4) - Chai Wah Wu, Apr 09 2015

Entry revised by N. J. A. Sloane, Apr 13 2015

Status

approved