A052091 Left parts needed for the construction of the palindromic prime pyramid starting with 2.

2, 7, 3, 33, 9, 30, 18, 92, 3, 133, 18, 117, 17, 15, 346, 93, 33, 180, 120, 194, 126, 336, 331, 330, 95, 12, 118, 369, 39, 32, 165, 313, 165, 134, 13, 149, 195, 145, 158, 720, 18, 396, 193, 102, 737, 964, 722, 156, 106, 395, 945, 303, 310, 113, 150, 303, 715, 123

Offset: 0

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

Comments

Each term is the smallest to have the previous term as a centered substring, beginning with the smallest palindromic prime 2. The right parts are the reversals of the above terms leading zeros included. The terms from a(34) onward currently correspond only to strong pseudoprimes.

For n > 0, the leftmost (most significant) digit of a(n) is either 1, 3, 7 or 9. - Chai Wah Wu, Dec 02 2015

Examples

			Start with 2; add 7 gives 727; add 3 gives 37273; add 33 gives 333727333; etc.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..501
• P. De Geest, World!Of Palindromic Primes, Page 3

Crossrefs

Cf. A053600, A052092, A047076.

Programs

Python

from sympy import isprime
A052091_list, p = [2], 2
for _ in range(30):
    m, ps = 1, str(p)
    s = int('1'+ps+'1')
    while not isprime(s):
        m += 1
        ms = str(m)
        if ms[0] in '268':
            ms = str(int(ms[0])+1) + '0'*(len(ms)-1)
            m = int(ms)
        if ms[0] in '45':
            ms = '7' + '0'*(len(ms)-1)
            m = int(ms)
        s = int(ms+ps+ms[::-1])
    p = s
    A052091_list.append(m) # Chai Wah Wu, Dec 02 2015

Extensions

Comments from G. L. Honaker, Jr., Mar 30 2000