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 A248051 Numbers whose cubes become squares if some digit is prepended, inserted or appended. 2
 1, 2, 5, 6, 10, 25, 30, 40, 41, 60, 84, 90, 96, 100, 121, 129, 160, 169, 200, 201, 250, 266, 360, 400, 490, 500, 600, 640, 724, 810, 1000, 1025, 1210, 1440, 1690, 1960, 2250, 2500, 2560, 2890, 3000, 3240, 3604, 3610, 4000, 4100, 4410, 4840, 5216, 5290, 5760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS No leading zeros allowed. Number of terms <= 10^k for k = 0, 1, 2, ...: 1, 5, 14, 31, 64, 144, 373, ..., . Robert G. Wilson v, Dec 27 2016 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..373 (terms 1..100 from Paolo P. Lava, terms 101..144 from Davin Park) EXAMPLE If n = 1 then n^3 = 1 and if we append a 6 we have sqrt(16) = 4. If n = 2 then n^3 = 8 and if we append a 1 we have sqrt(81) = 9. If n = 5 then n^3 = 125 and if we insert a 2 we get sqrt(1225) = 35. Again, if n = 25 then n^3 = 15625 and we have sqrt(105625) = 325 or sqrt(156025) = 395. MAPLE with(numtheory): P:=proc(q) local a, b, j, k, n, ok; for n from 1 to q do a:=n^3; b:=ilog10(a)+1; ok:=1; for k from 0 to b do if ok=1 then for j from 0 to 9 do if not (j=0 and k=b) then if type(sqrt(trunc(a/10^k)*10^(k+1)+j*10^k+(a mod 10^k)), integer) then print(n); ok:=0; break; fi; fi; od; fi; od; od; end: P(10^6); MATHEMATICA f[n_] := ! MissingQ@SelectFirst[Rest@Flatten[Outer[Insert[IntegerDigits[n^3], #2, #1] &, Range[IntegerLength[n^3] + 1], Range[0, 9]], 1], IntegerQ@Sqrt@FromDigits@# &]; Select[Range[100], f] (* Davin Park, Dec 28 2016 *) CROSSREFS Cf. A248127, A249853. Sequence in context: A123645 A057252 A057250 * A056643 A057256 A236248 Adjacent sequences:  A248048 A248049 A248050 * A248052 A248053 A248054 KEYWORD nonn,base AUTHOR Paolo P. Lava, Nov 10 2014 EXTENSIONS Corrected and extended by Davin Park, Dec 26 2016 Extended by Robert G. Wilson v, Dec 27 2016 STATUS approved

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Last modified January 25 19:09 EST 2020. Contains 331249 sequences. (Running on oeis4.)