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A307752
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Number of n-digit palindromic pentagonal numbers.
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2
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3, 1, 0, 2, 1, 1, 2, 2, 0, 4, 0, 0, 3, 1, 1, 1, 3, 2, 4, 1, 3, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Number of n-digit terms in A002069.
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LINKS
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G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.
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EXAMPLE
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There are only two 4-digit pentagonal number that are palindromic, 1001 and 2882. Thus, a(4)=2.
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MATHEMATICA
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A002069 = {0, 1, 5, 22, 1001, 2882, 15251, 720027, 7081807, 7451547, 26811862, 54177145, 1050660501, 1085885801, 1528888251, 2911771192, 2376574756732, 5792526252975, 5875432345785, 10810300301801, 264571020175462, 5292834004382925, 10808388588380801, 15017579397571051, 76318361016381367, 150621384483126051, 735960334433069537, 1003806742476083001, 1087959810189597801, 2716280733370826172};
Table[Length[Select[A002069, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 18}] (* Robert Price, Apr 26 2019 *)
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PROG
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(Python)
def afind(terms):
m, n, c = 0, 1, 0
while n <= terms:
p = m*(3*m-1)//2
s = str(p)
if len(s) == n:
if s == s[::-1]: c += 1
else:
print(c, end=", ")
n, c = n+1, int(s == s[::-1])
m += 1
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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