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A003166 Numbers whose square in base 2 is a palindrome.
(Formerly M3181)
13
0, 1, 3, 4523, 11991, 18197, 141683, 1092489, 3168099, 6435309, 12489657, 17906499, 68301841, 295742437, 390117873, 542959199, 4770504939, 17360493407, 73798050723, 101657343993, 107137400475, 202491428745, 1615452642807 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No,1, 1972), 11-19.

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

LINKS

Jon E. Schoenfield and Don Knuth, Table of n, a(n) for n = 1..34

P. De Geest, Palindromic Squares

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

EXAMPLE

3^2 = 9 = 1001 (base 2) = palindrome.

MATHEMATICA

Do[c = RealDigits[n^2, 2][[1]]; If[c == Reverse[c], Print[n]], {n, 0, 10^9}]

PROG

(PARI) is(n)=my(b=binary(n^2)); b==Vecrev(b) \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A002778 (base 10 analog), A029983 (the actual squares). In binary: A262595, A262596.

Sequence in context: A024048 A094319 A229766 * A251603 A168556 A200950

Adjacent sequences:  A003163 A003164 A003165 * A003167 A003168 A003169

KEYWORD

base,nonn,hard,nice

AUTHOR

N. J. A. Sloane, R. H. Hardin

EXTENSIONS

a(16) = 4770504939 found by Patrick De Geest, May 15 1999

a(17) through a(31) from Jon E. Schoenfield, May 08 2009

a(32) = 285000288617375,

a(33) = 301429589329949,

a(34) = 1178448744881657 from Don Knuth, Jan 28 2013 [who doublechecked the previous results and searched up to 2^104]

STATUS

approved

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Last modified June 29 05:29 EDT 2017. Contains 288859 sequences.