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 A116098 Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 6. 6
 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Robert Israel, Aug 13 2018: (Start) Contained in, and apparently identical, to A116129. Numbers k such that k*(10^d+1) is a square, where k-9 has d decimal digits. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..134 EXAMPLE 100000001//99999992 = 99999998 * 100000004, where // denotes concatenation. MAPLE g:= proc(d) local r, c, a, b; r:= mul(t[1], t=select(s -> s[2]::odd, ifactors(10^d+1)[2])) c:= ceil((10^(d-1)+9)/r); a:= isqrt(c); if a^2 < c then a:= a+1 fi; c:= floor((10^d+8)/r); b:= isqrt(c); if b^2 > c then b:= b-1 fi; seq(r*y^2, y = a..b) end proc: seq(g(d), d=1..60); # Robert Israel, Aug 13 2018 CROSSREFS Cf. A116097, A116099, A116106, A054214, A116128, A116129, A116130, A116136, A116229, A116260. Sequence in context: A191420 A118937 A031997 * A116129 A056810 A000533 Adjacent sequences: A116095 A116096 A116097 * A116099 A116100 A116101 KEYWORD nonn,base AUTHOR Giovanni Resta, Feb 06 2006 STATUS approved

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Last modified August 15 12:22 EDT 2024. Contains 375173 sequences. (Running on oeis4.)