A237913 - OEIS

A237913

Smallest number m > 1 (not ending in a 0) such that m and the digit reversal of m have n prime factors (counted with multiplicity). Palindromes are included.

2, 4, 8, 88, 252, 2576, 21708, 2112, 4224, 8448, 44544, 48384, 2977792, 21989376, 405504, 4091904, 441606144, 405909504, 886898688, 677707776, 4285005824, 276486684672, 21128282112, 633498894336, 2701312131072, 6739855589376, 29142024192, 65892155129856, 4815463645184, 445488555884544

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

OFFSET

1,1

LINKS

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

FORMULA

a(n) = min{A076886(n+1), A237912(n)}

EXAMPLE

252 is the smallest number such that 252 and its reverse (also 252) have 5 prime factors (2*2*3*3*7). So, a(5) = 252.

2576 is the smallest number such that 2576 and its reverse (6752) have 6 prime factors (2*2*2*2*7*23 and 2*2*2*2*2*211, respectively). So a(6) = 2576.

PROG

(Python)

import sympy

from sympy import factorint

def rev(x):

rev = ''

for i in str(x):

rev = i + rev

return int(rev)

def RevFact(x):

n = 2

while n < 10**8:

if n % 10 != 0:

if sum(list(factorint(n).values())) == x:

if sum(list(factorint(rev(n)).values())) == x:

return n

else:

n += 1

else:

n += 1

else:

n += 1

x = 1

while x < 100:

print(RevFact(x))

x += 1

CROSSREFS

Cf. A004086, A076886, A237912.

Sequence in context: A088114 A348050 A239697 * A076886 A309565 A046385

Adjacent sequences: A237910 A237911 A237912 * A237914 A237915 A237916

KEYWORD

nonn,base

AUTHOR

Derek Orr, Feb 15 2014

EXTENSIONS

a(17)-a(21) from Giovanni Resta, Feb 23 2014

a(22)-a(30) from Max Alekseyev, Feb 08 2024

STATUS

approved