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A339978
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a(n) is the largest prime whose decimal expansion consists of the concatenation of a 1-digit square, a 2-digit square, a 3-digit square, ..., and an n-digit square, or 0 if there is no such prime.
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9
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0, 449, 981961, 9819619801, 981961980196721, 981961980199856194481, 9819619801998569980018946081, 981961980199856998001999824499740169, 981961980199856998001999824499980001989039601, 9819619801998569980019998244999800019999508849977812321
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OFFSET
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1,2
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COMMENTS
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If a(n) exists it has A000217(n)= n*(n+1)/2 digits.
All the terms end with 1 or 9.
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LINKS
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EXAMPLE
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a(1) = 0 because no 1-digit square {0, 1, 4, 9} is prime.
a(2) = 449 because 464, 481, 916, 925, 936, 949, 964, and 981 are not primes and 449, concatenation of 4 = 2^2 with 49 = 7^2, is prime.
a(4) = 9819619801, which is a prime is the concatenation of 9 = 3^2 with 81 = 9^2, then 961 = 31^2 and 9801 = 99^2. Observation, 9, 81, 961 and 9801 are the largest squares with respectively 1, 2, 3 and 4 digits.
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PROG
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(Python)
from sympy import isprime
from itertools import product
def a(n):
squares = [str(k*k) for k in range(1, int((10**n)**.5)+2)]
revsqrs = [[kk for kk in squares if len(kk)==i+1][::-1] for i in range(n)]
for t in product(*revsqrs):
intt = int("".join(t))
if isprime(intt): return intt
return 0
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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