A002993 Initial digits of squares.

0, 1, 4, 9, 1, 2, 3, 4, 6, 8, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Gelfand's Question

Crossrefs

Cf. A000030, A000290, A089951, A002994.

Programs

Haskell

a002993 = a000030 . a000290  -- Reinhard Zumkeller, Apr 01 2015

Maple

a:= n-> parse(""||(n^2)[1]):
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 06 2021

Mathematica

a[n_] := First[IntegerDigits[n^2]]; Table[a[n], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Dec 21 2008 *)
First[IntegerDigits[#]]&/@(Range[70]^2) (* Harvey P. Dale, Feb 09 2011 *)

Formula

a(n) = A000030(A000290(n)). - Reinhard Zumkeller, Aug 17 2008