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 A115556 Numbers whose square is the concatenation of two numbers 9*m and m. 30
 12857142857142857142857142857142857143, 25714285714285714285714285714285714286, 117391304347826086956521739130434782608695652173913043478261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(4)=156521739130434782608695652173913043478260869565217391304348. From Robert Israel, Aug 24 2023: (Start) If 9 * 10^d + 1 = a^2 * b with a > 1, then a * b * c is a term if a^2/(90 + 10^(1-d)) < c^2 < a^2/(9 + 10^(-d)). For example, 9 * 10^d + 1 is divisible by 7^2 for d == 37 (mod 42), and then (9 * 10^d + 1)/7 and 2*(9 * 10^d + 1)/7 are terms. In particular, the sequence is infinite. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..12 MAPLE F:= proc(d) local R, F, t, b, r, q, s, m0, x0, k; R:= NULL; F:= ifactors(9*10^d+1)[2]; b:= mul(t[1]^floor(t[2]/2), t=F); for r in numtheory:-divisors(b) do x0:= (9*10^d+1)/r; m0:= x0/r; for k from ceil(sqrt(10^(d-1)/m0)) to floor(sqrt(10^d/m0)) do R:= R, x0*k; od od; R end proc: sort(map(F, [\$1..90])); # Robert Israel, Aug 24 2023 CROSSREFS Cf. A009474, A102567, A106497, A115527 - A115555. Sequence in context: A217419 A246289 A095468 * A173907 A095470 A329659 Adjacent sequences: A115553 A115554 A115555 * A115557 A115558 A115559 KEYWORD nonn,base,bref AUTHOR Giovanni Resta, Jan 25 2006 EXTENSIONS Definition modified by Georg Fischer, Jul 26 2019 STATUS approved

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Last modified September 28 02:54 EDT 2023. Contains 365714 sequences. (Running on oeis4.)