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A052091
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Left parts needed for the construction of the palindromic prime pyramid starting with 2.
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5
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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Start with 2; add 7 gives 727; add 3 gives 37273; add 33 gives 333727333; etc.
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PROG
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(Python)
from sympy import isprime
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
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CROSSREFS
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KEYWORD
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nonn,base,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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