A053600 - OEIS

A053600

a(1) = 2; for n>=1, a(n+1) is the smallest palindromic prime with a(n) as a central substring.

2, 727, 37273, 333727333, 93337273339, 309333727333903, 1830933372733390381, 92183093337273339038129, 3921830933372733390381293, 1333921830933372733390381293331, 18133392183093337273339038129333181

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

G. L. Honaker, Jr. and Chris K. Caldwell, Palindromic Prime Pyramids, J. Recreational Mathematics, Vol. 30(3) 169-176, 1999-2000.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..200

P. De Geest, Palindromic Prime Pyramid Puzzle by G.L.Honaker,Jr

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 18133...33181 (35-digits)

G. L. Honaker, Jr. & C. K. Caldwell, Palindromic Prime Pyramids

G. L. Honaker, Jr. & C. K. Caldwell, Supplement to "Palindromic Prime Pyramids"

Ivars Peterson, Primes, Palindromes, and Pyramids, Science News.

Inder J. Taneja, Palindromic Prime Embedded Trees, RGMIA Res. Rep. Coll. 20 (2017), Art. 124.

Inder J. Taneja, Same Digits Embedded Palprimes, RGMIA Research Report Collection (2018) Vol. 21, Article 75, 1-47.

EXAMPLE

As a triangle:

.........2

........727

.......37273

.....333727333

....93337273339

..309333727333903

1830933372733390381

MATHEMATICA

d[n_] := IntegerDigits[n]; t = {x = 2}; Do[i = 1; While[! PrimeQ[y = FromDigits[Flatten[{z = d[i], d[x], Reverse[z]}]]], i++]; AppendTo[t, x = y], {n, 10}]; t (* Jayanta Basu, Jun 24 2013 *)

PROG

(Python)

from gmpy2 import digits, mpz, is_prime

A053600_list, p = [2], 2

for _ in range(30):

m, ps = 1, digits(p)

s = mpz('1'+ps+'1')

while not is_prime(s):

m += 1

ms = digits(m)

s = mpz(ms+ps+ms[::-1])

p = s