cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A262615 Amicable digital pairs: A262091 and A262092 interleaved.

Original entry on oeis.org

136, 244, 919, 1459, 2178, 6514, 58618, 76438, 89883, 157596, 63804, 313625, 2755907, 6586433, 8139850, 9057586, 144839908, 1043820406, 277668893, 756738746, 304162700, 344050075, 4370652168, 11346057072, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387
Offset: 1

Views

Author

Omar E. Pol, Nov 29 2015

Keywords

Comments

A pair of numbers x and y are called amicable digital if, 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.
First differs from A264958 (another version) at a(9).

Crossrefs

Extensions

Suggested by Don Knuth, see the Links section and A262091.

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.

Original entry on oeis.org

136, 919, 2178, 58618, 89883, 63804, 2755907, 8139850, 144839908, 277668893, 304162700, 4370652168, 21914086555935085, 187864919457180831, 13397885590701080090, 19095442247273220984552, 108493282045082839040458, 1553298727699254868304830
Offset: 1

Views

Author

Don Knuth, Sep 10 2015

Keywords

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

Examples

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

Crossrefs

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

Programs

  • 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

Extensions

Definition clarified by Chai Wah Wu, Jan 04 2016

A264951 Amicable digital numbers.

Original entry on oeis.org

136, 244, 919, 1459, 2178, 6514, 58618, 63804, 76438, 89883, 157596, 313625, 2755907, 6586433, 8139850, 9057586, 144839908, 277668893, 304162700, 344050075, 756738746, 1043820406, 4370652168, 11346057072, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387
Offset: 1

Views

Author

Omar E. Pol, Nov 29 2015

Keywords

Comments

Union of A262091 and A262092.
Numbers of A262615 in increasing order.
Numbers of A264958 in increasing order.
For amicable digital pairs see A262615 and also A264958.
First differs from A262615 at a(8).
First differs from A264958 at a(8).
For more information see A262091.

References

  • K. Oséki, A problem of number theory, Proceedings of the Japan Academy 36 (1960), 578-587.

Crossrefs

A264958 Amicable digital pair: the pairs from A262615 ordered by their smallest member.

Original entry on oeis.org

136, 244, 919, 1459, 2178, 6514, 58618, 76438, 63804, 313625, 89883, 157596, 2755907, 6586433, 8139850, 9057586, 144839908, 1043820406, 277668893, 756738746, 304162700, 344050075, 4370652168, 11346057072, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387
Offset: 1

Views

Author

Omar E. Pol, Nov 29 2015

Keywords

Comments

First differs from A262615 (another version) at a(9).

Crossrefs

Showing 1-4 of 4 results.