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A089951 Numbers having the same leading decimal digits as their squares. 6
0, 1, 10, 11, 12, 13, 14, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 895 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A000030(a(n)) = A002993(a(n)) = A000030(A000290(a(n))).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

A number n is in the sequence iff n = 0 or n/10^[log10(n)] lies in one of the half-open intervals [1, sqrt(2)), [sqrt(80), 9) or [sqrt(90), 10). - David W. Wilson, May 29 2008

EXAMPLE

895*895 = 801025, therefore 895 is a term: a(55)=895.

MAPLE

F:= proc(d) $10^d .. floor(sqrt(2)*10^d), $ ceil(sqrt(80)*10^d) .. 9*10^d - 1, $ ceil(sqrt(90)*10^d) .. 10^(d+1)-1 end proc:

0, F(0), F(1), F(2), F(3); # Robert Israel, Mar 18 2015

MATHEMATICA

d[n_] := IntegerDigits[n]; Select[Range[895],

First[d[#]] == First[d[#^2]] &] (* Jayanta Basu, Jun 03 2013 *)

PROG

(PARI) a(n)={my(v = [1, sqrt(80), sqrt(90)], w=[(k)->10^k * ((sqrt(2) - 1))\1 + 1, (k)->9 * 10^k - ceil(sqrt(80) * 10^k), (k)->10 * 10^k - ceil(sqrt(90) * 10^k)], i = 1, k = 0); if(n==1, 0, n--; while(n>w[i](k), n-=w[i](k); i++; if(i == 4, i = 1; k++)); ceil(v[i]*10^k)+n-1)} \\ David A. Corneth, Feb 26 2015

(PARI) isok(n) = (n == 0) || (digits(n)[1] == digits(n^2)[1]); \\ Michel Marcus, Mar 18 2015

(Haskell)

a089951 n = a089951_list !! (n-1)

a089951_list = [x | x <- [0..], a000030 x == a000030 (x ^ 2)]

-- Reinhard Zumkeller, Apr 01 2015

CROSSREFS

Cf. A018834.

Cf. A144582. - Reinhard Zumkeller, Aug 17 2008

Cf. A000030, A002993, A000290, A256523 (subsequence).

Sequence in context: A228774 A073527 A008707 * A058945 A270040 A072554

Adjacent sequences:  A089948 A089949 A089950 * A089952 A089953 A089954

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Jan 12 2004

STATUS

approved

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Last modified February 24 22:37 EST 2018. Contains 299627 sequences. (Running on oeis4.)