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 A339978 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. 9
 0, 449, 981961, 9819619801, 981961980196721, 981961980199856194481, 9819619801998569980018946081, 981961980199856998001999824499740169, 981961980199856998001999824499980001989039601, 9819619801998569980019998244999800019999508849977812321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If a(n) exists it has A000217(n)= n*(n+1)/2 digits. All the terms end with 1 or 9. LINKS David A. Corneth, Table of n, a(n) for n = 1..40 (first 16 terms from Michael S. Branicky) EXAMPLE 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. PROG (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 print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Dec 25 2020 CROSSREFS Cf. A000290, A003618, A061433 (largest squares), A338968 (concatenate primes). Sequence in context: A012169 A093402 A012062 * A079659 A304511 A202197 Adjacent sequences:  A339975 A339976 A339977 * A339979 A339980 A339981 KEYWORD nonn,base AUTHOR Bernard Schott, Dec 25 2020 EXTENSIONS a(5)-a(10) from Michael S. Branicky, Dec 25 2020 STATUS approved

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Last modified August 5 08:27 EDT 2021. Contains 346464 sequences. (Running on oeis4.)