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

Offset: 1

Author

G. L. Honaker, Jr., Jan 20 2000

Keywords

• base
• nonn

Examples

			As a triangle:
.........2
........727
.......37273
.....333727333
....93337273339
..309333727333903
1830933372733390381
		

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.

Crossrefs

Cf. A000040, A002385, A047076, A052205, A034276, A256957, A052091, A052092, A261881.

Programs

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 *)

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
    A053600_list.append(int(p)) # Chai Wah Wu, Apr 09 2015