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A262091 Amicable digital pairs: The smaller number of a pair (x,y) with x <> y such that, in decimal notation and with an appropriate number of leading zeros prepended, x=(x_m...x_1x_0)_{10}, y=(y_m...y_1y_0)_{10}, x = y_m^m + ... + y_1^m + y_0^m, and y = x_m^m + ... + x_1^m + x_0^m. 4
136, 919, 2178, 58618, 89883, 63804, 2755907, 8139850, 144839908, 277668893, 304162700, 4370652168, 21914086555935085, 187864919457180831, 13397885590701080090, 19095442247273220984552, 108493282045082839040458, 1553298727699254868304830 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If we allow x to be equal to y we get numbers such as 1, 153, 370, 371, 407, ... See A252648. - Chai Wah Wu, Jan 04 2016

LINKS

Table of n, a(n) for n=1..18.

D. Knuth, Table of a(n) and its mate for n=1..36

K. Os├ęki, A problem of number theory, Proceedings of the Japan Academy 36 (1960), 578-587.

EXAMPLE

a(1) is amicably paired to 244, because 1^3 + 3^3 + 6^3 = 244 and 2^3 + 4^3 + 4^3 = 136.

PROG

(Python)

# print pairs with leading zeros

from __future__ import print_function

from itertools import combinations_with_replacement

for m in range(2, 11):

    fs = '0'+str(m+1)+'d'

    for c in combinations_with_replacement(range(10), m+1):

        n = sum(d**m for d in c)

        r = sum(int(q)**m for q in str(n))

        rlist = sorted(int(d) for d in str(r))

        rlist = [0]*(m+1-len(rlist))+rlist

        if n < r and rlist == list(c):

            print(format(n, fs), format(r, fs)) # Chai Wah Wu, Jan 04 2016

CROSSREFS

A262092 has the larger element of each pair. Cf. A252648.

Sequence in context: A270341 A234169 A234162 * A251175 A251168 A023070

Adjacent sequences:  A262088 A262089 A262090 * A262092 A262093 A262094

KEYWORD

nonn,base

AUTHOR

Don Knuth, Sep 10 2015

EXTENSIONS

Definition clarified by Chai Wah Wu, Jan 04 2016

STATUS

approved

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Last modified October 21 19:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)