A009944 Left-right/right-left numbers: n = pq such that n=q_reversed*p_reversed.

126, 153, 688, 187029, 223524, 267034, 1574253, 10013323, 10353244, 36528975, 109019911, 116257833, 1958249722, 2285044524, 2996225824, 6264507888, 10544814252, 15742574253, 31951523916, 35497206387, 62967699976, 94691579179, 182738252812, 187021087029

Offset: 1

Author

Mario Velucchi (mathchess(AT)velucchi.it)

Keywords

• base
• nonn
• nice

Comments

The decimal expansion of n is p followed by q, and n is also the product of R(p)*R(q), where R reverses the order of the digits. - N. J. A. Sloane, May 22 2016

A subset of A179482; only two factors permitted. - Adam Kertesz, Aug 07 2010

The sequence is infinite, since it contains at least 3 infinite subsequences, namely b(n) = 3*(88810 + 2099*10^(6*n))/33670 = 187029, 187021087029,... c(n) = 11011*(1 + 100^(1 + 2*n))/101 = 109019911, 1090198019911,... and d(n) = 3*(53*10000^n - 14900)/10100 = 153, 1574253,... - Giovanni Resta, Mar 17 2013

Examples

			E.g. 223524 = 42 * 5322.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..30

Crossrefs

Cf. A004086, A179482.

Programs

Mathematica

Reap[For[n = 1, n < 2*10^8, n++, For[dd = IntegerDigits[n] // Reverse; k = 1, k <= Length[dd] - 1, k++, If[n == FromDigits[dd[[1 ;; k]]]*FromDigits[ dd[[k + 1 ;; -1]]], Print[n]; Sow[n]; Break[]]]]][[2, 1]] (* Jean-François Alcover, May 22 2016 *)

Python

from sympy import divisors
def ok(n):
    if n%10==0: return False
    t = str(n)[::-1]
    return any(t==str(d)+str(n//d) for d in divisors(n, generator=True))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Apr 13 2024

Extensions

David W. Wilson has verified that all terms shown are correct, Sep 28 2000