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

1,1

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

Crossrefs

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

Sequence in context: A062066 A174368 A082621 * A090275 A090565 A332172

Adjacent sequences: A053597 A053598 A053599 * A053601 A053602 A053603

Keyword

base,nonn

Author

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

Status

approved