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

0,1

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

Links

Chai Wah Wu, Table of n, a(n) for n = 0..501

P. De Geest, World!Of Palindromic Primes, Page 3

Example

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

Prog

(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

Crossrefs

Cf. A053600, A052092, A047076.

Sequence in context: A210662 A229610 A117809 * A090276 A249782 A090564

Adjacent sequences: A052088 A052089 A052090 * A052092 A052093 A052094

Keyword

nonn,base,changed

Author

Patrick De Geest, Jan 15 2000

Extensions

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

Status

approved