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A083408
Squares which can be expressed as the product of a number and its reversal in at least two different ways.
11
63504, 435600, 6350400, 7683984, 16240900, 25401600, 43560000, 66585600, 420332004, 558471424, 635040000, 647804304, 726949444, 768398400, 782432784, 1067328900, 1624090000, 1897473600, 2341011456, 2540160000, 4356000000, 6658560000, 42033200400, 50860172484, 52587662400
OFFSET
1,1
COMMENTS
Union of A083406 and A083407. - Lekraj Beedassy, Apr 23 2006
REFERENCES
S. S. Gupta, EPRNs, Science Today, Feb. 1987, India.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..2498 (n = 1..76 from Hans Havermann, n = 77..241 from David A. Corneth)
Shyam Sunder Gupta, EPRN Numbers.
Shyam Sunder Gupta, Equal Product of Reversible Numbers (EPRN), Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 12, 353-365.
EXAMPLE
63504 = 252 * 252 = 144 * 441,
1239016098321 = 1113111 * 1113111 = 1022121 * 1212201, etc.
635040000 = 144 * 4410000 = 252 * 2520000 = 441 * 1440000. - David A. Corneth, Mar 22 2019
PROG
(PARI) is(n) = {if(!issquare(n), return(0)); my(d = divisors(n), t = 0); forstep(i = #d, #d \ 2 + 1, -1, revd = fromdigits(Vecrev(digits(d[i]))); if(revd * d[i] == n, t++; if(t >= 2, return(1)); ) ); 0 } \\ David A. Corneth, Mar 21 2019
CROSSREFS
Cf. A062917, A066531, A083406 (even), A083407 (odd), A070760, A117281 (palindromic square roots), A206642 (non-palindromic square roots), A325150 (products in exactly two different ways), A307019 (products in exactly three different ways).
Sequence in context: A117282 A076750 A083406 * A325150 A072693 A119276
KEYWORD
nonn,base
AUTHOR
Shyam Sunder Gupta, Jun 07 2003
EXTENSIONS
Corrected and extended by Hans Havermann, Feb 11 2012
a(21)-a(25) from David A. Corneth, Mar 21 2019
Definition corrected by N. J. A. Sloane, Aug 01 2019
STATUS
approved