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A052091
Left parts needed for the construction of the palindromic prime pyramid starting with 2.
5
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
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
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Jan 15 2000
EXTENSIONS
Comments from G. L. Honaker, Jr., Mar 30 2000
STATUS
approved