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.

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A370255 (n*10)^(n*10) omitting its rightmost trailing 0's.

Original entry on oeis.org

1, 1, 1048576, 205891132094649, 1208925819614629174706176, 88817841970012523233890533447265625, 48873677980689257489322752273774603865660850176, 143503601609868434285603076356671071740077383739246066639249
Offset: 0

Views

Author

Marco Ripà, Feb 13 2024

Keywords

Examples

			a(0) = A004151(0^0) = A004151(1) = 1.
a(2) = 1048576 since 20^20 = 104857600000000000000000000.

Links

Crossrefs

Cf. A000312, A002489, A004151, A008592, A369771, A369826.

Programs

  • Python
    def A370255(n):
    if n == 0: return 1
    m = n
    a, b = divmod(m,10)
    while not b:
        m = a
        a, b = divmod(m,10)
    return m**(10*n) # Chai Wah Wu, Feb 20 2024

Formula

a(n) = A004151((n*10)^(n*10)).
a(n) = A004151(n)^(n*10), for n >= 1.

A379512 Erase digits 0 and 1 from decimal expansion of n. Then keep just the coprime digits; write 0 if all digits disappear.

Original entry on oeis.org

0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 0, 23, 0, 25, 0, 27, 0, 29, 3, 3, 32, 0, 34, 35, 0, 37, 38, 0, 4, 4, 0, 43, 0, 45, 0, 47, 0, 49, 5, 5, 52, 53, 54, 0, 56, 57, 58, 59, 6, 6, 0, 0, 0, 65, 0, 67, 0, 0, 7, 7, 72, 73, 74, 75, 76, 0, 78, 79, 8, 8, 0, 83, 0, 85, 0, 87
Offset: 0

Views

Author

Ctibor O. Zizka, Jan 21 2025

Keywords

Comments

The numbers n such that a(n) = k for any fixed k are a 10-automatic sequence. - Charles R Greathouse IV, Jan 21 2025

Examples

			a(10) = 0 as we do not accept zeros and ones in n.
a(22) = 0 as gcd(2,2) = 2.
a(25) = 25 as gcd(2,5) = 1.
a(1234567890) = a(23456789) = a(3579) = a(57) = 57.
Note that numbers n with even digits and numbers n containing digits 0 and 1 only disappear immediately and we get a(n) = 0.

Crossrefs

Cf. A004151, A004719, A059717.

Programs

  • PARI
    a(n)=my(d=select(k->k>1, digits(n))); if(sum(i=1,#d, d[i]%2==0)>1, d=select(k->k%2,d)); if(sum(i=1,#d, d[i]%3==0)>1, d=select(k->k%3,d)); if(sum(i=1,#d, d[i]==5)>1, d=select(k->k!=5,d)); if(sum(i=1,#d, d[i]==7)>1, d=select(k->k!=7,d)); fromdigits(d) \\ Charles R Greathouse IV, Jan 21 2025

Formula

a(n) <= 9875. There are 299 distinct values in this sequence. - Charles R Greathouse IV, Jan 21 2025
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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