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 A035237 Smallest number that has exactly n substrings which are square. 0
 2, 0, 10, 49, 100, 1000, 1441, 4900, 11449, 104900, 144100, 490000, 1440000, 1144900, 11144900, 16810000, 114490049, 156250000, 114490000, 1114490000, 1681000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS No leading 0's allowed in substrings, except for the number 0. a(15+5k+j) <= 1681*10^(4+2k+j) for j = 0, 1. In particular, a(21) <= 16810000000. Similar upper bounds can be derived using numbers of the form 49*10^k, 144*10^k, 1149*10^k, etc. - Michael S. Branicky, Dec 15 2020 LINKS Table of n, a(n) for n=0..20. EXAMPLE a(3)=49 since 4, 9 and 49 are squares and no smaller number works. PROG (Python) LIMIT = 10**7 ss = set(str(i*i) for i in range(int(LIMIT**.5)+2)) def num_square_substrings(s): return sum(s[i:j] in ss for i in range(len(s)) for j in range(i+1, len(s)+1)) def agen(): n, k, data = 0, 0, dict() while True: if n in data: yield data[n]; n += 1; continue while True: if k > LIMIT: assert False, "LIMIT exceeded" nss = num_square_substrings(str(k)) if nss == n: data[n] = k; yield k; break elif nss > n: if nss not in data: data[nss] = k k += 1 n += 1 g = agen() for i in range(13): print(next(g)) # Michael S. Branicky, Dec 15 2020 CROSSREFS Cf. A035222. Sequence in context: A065624 A086890 A167387 * A189423 A342287 A230696 Adjacent sequences: A035234 A035235 A035236 * A035238 A035239 A035240 KEYWORD nonn,base,more AUTHOR Erich Friedman EXTENSIONS a(0) corrected, a(8)-a(14) added, and title made more specific by Sean A. Irvine, Oct 01 2020 a(15)-a(20) from Michael S. Branicky, Dec 15 2020 STATUS approved

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Last modified December 11 06:34 EST 2023. Contains 367717 sequences. (Running on oeis4.)