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A053600 a(1) = 2; for n>=1, a(n+1) is the smallest palindromic prime with a(n) as a central substring. 10
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.

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 A072384

Adjacent sequences:  A053597 A053598 A053599 * A053601 A053602 A053603

KEYWORD

base,nonn

AUTHOR

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

STATUS

approved

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Last modified January 22 22:38 EST 2018. Contains 298093 sequences.