A086457 - OEIS

A086457

Both n and n^2 have the same initial digit and also n and n^2 have the same final digit when expressed in base 10.

0, 1, 10, 11, 95, 96, 100, 101, 105, 106, 110, 111, 115, 116, 120, 121, 125, 126, 130, 131, 135, 136, 140, 141, 895, 896, 950, 951, 955, 956, 960, 961, 965, 966, 970, 971, 975, 976, 980, 981, 985, 986, 990, 991, 995, 996, 1000, 1001, 1005, 1006, 1010, 1011

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

All terms of A045953 appear in this sequence.

Subsequence of A008851; A045953 and A046851 are subsequences. [Reinhard Zumkeller, Jul 27 2011]

Intersection of A008851 and A089951. - Michel Marcus, Mar 19 2015

LINKS

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

FORMULA

A000030(a(n)) = A000030(a(n)^2) and A010879(a(n)) = A010879(a(n)^2).

EXAMPLE

a(12) = 115 appears in the sequence because 115*115 = 13225.

MATHEMATICA

ldQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[n^2]}, First[ idn] == First[idn2]&&Last[idn]==Last[idn2]]; Select[Range[ 0, 1100], ldQ] (* Harvey P. Dale, Feb. 06 2011 *)

PROG

(BASIC)

left$(str$(n), 1) = left$(str$(n^2), 1) AND right$(str$(n), 1) = right$(str$(n^2), 1)

(Haskell)

a086457 n = a086457_list !! (n-1)

a086457_list = filter (\x -> a000030 x == a000030 (x^2) &&

a010879 x == a010879 (x^2)) [0..]

-- Reinhard Zumkeller, Jul 27 2011

CROSSREFS

Cf. A045953, A086458.

Sequence in context: A262229 A347182 A331604 * A046851 A045953 A136830

Adjacent sequences: A086454 A086455 A086456 * A086458 A086459 A086460