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.

A333410 a(n) is the smallest positive integer not yet appearing in the sequence such that n*a(n) contains n as a substring.

Original entry on oeis.org

1, 6, 10, 11, 3, 16, 21, 23, 22, 31, 100, 26, 87, 51, 41, 73, 69, 66, 63, 36, 58, 101, 97, 52, 5, 102, 103, 46, 79, 61, 107, 76, 192, 151, 81, 38, 201, 89, 164, 35, 59, 34, 173, 126, 99, 184, 74, 135, 153, 7, 167, 176, 29, 251, 121, 28, 168, 148, 27, 56, 92, 123, 137, 57, 141, 207, 25, 113
Offset: 1

Views

Author

Scott R. Shannon, Apr 11 2020

Keywords

Examples

			a(2) = 6 as 6 has not appeared previously and 2 * 6 = 12 which contains '2' as a substring.
a(6) = 16 as 16 has not appeared previously and 6 * 16 = 96 which contains '6' as a substring.
a(7) = 21 as 21 has not appeared previously and 7 * 21 = 147 which contains '7' as a substring.

Links

Crossrefs

Cf. A086064, A333774, A333775, A333811, A332795, A332703.

Programs

  • PARI
    See Links section.
  • Python
    from itertools import count, islice
def agen(): # generator of terms
    s, mink, aset, concat = 1, 2, {1}, "1"
    yield from [1]
    for n in count(2):
        an, sn = mink, str(n)
        while an in aset or not sn in str(n*an): an += 1
        aset.add(an); s += an; concat += str(an); yield an
        while mink in aset: mink += 1
print(list(islice(agen(), 68))) # Michael S. Branicky, Feb 08 2024

A333811 a(0) = 0; for n > 0, a(n) is the smallest positive integer not yet appearing in the sequence such that a(n-1)^a(n) contains as a substring either a(n-1) or a(n).

Original entry on oeis.org

0, 1, 2, 5, 3, 7, 4, 6, 8, 9, 11, 15, 12, 14, 13, 10, 16, 17, 21, 20, 25, 18, 23, 19, 22, 24, 26, 29, 30, 28, 31, 27, 32, 33, 35, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 46, 48, 50, 49, 51, 52, 53, 55, 54, 56, 57, 59, 58, 61, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70
Offset: 0

Views

Author

Scott R. Shannon, Apr 05 2020

Keywords

Comments

a(3) = 5 as a(2) ^ a(3) = 2 ^ 5 = 32 which contains '2' as a substring.
a(4) = 3 as a(3) ^ a(4) = 5 ^ 3 = 125 which contains '5' as a substring.
a(5) = 7 as a(4) ^ a(5) = 3 ^ 7 = 2187 which contains '7' as a substring.

Links

Crossrefs

Cf. A333774, A333775, A332795, A332703.

Programs

  • PARI
    See Links section.

A333775 a(0) = 0; for n > 0, a(n) is the smallest positive integer not yet appearing in the sequence such that a(n-1) * a(n) contains as a substring either a(n-1) or a(n).

Original entry on oeis.org

0, 1, 2, 6, 4, 10, 3, 5, 7, 11, 8, 16, 20, 21, 9, 22, 51, 12, 26, 24, 52, 76, 28, 46, 40, 31, 30, 41, 15, 50, 13, 25, 17, 69, 34, 42, 94, 100, 14, 82, 71, 60, 36, 38, 89, 55, 61, 35, 80, 56, 87, 33, 75, 29, 53, 101, 18, 66, 151, 32, 91, 43, 102, 19, 63, 137, 83, 96, 126, 44, 59, 27, 103
Offset: 0

Views

Author

Scott R. Shannon, Apr 05 2020

Keywords

Examples

			a(1) = 1 as a(0) * a(1) = 0 * 1 = 0 which contains '0' as a substring.
a(4) = 4 as a(3) * a(4) = 6 * 4 = 24 which contains '4' as a substring.
a(18) = 26 as a(17) * a(18) = 12 * 26 = 312 which contains '12' as a substring.

Links

Crossrefs

Cf. A333774, A333811, A332795, A332703.

Programs

  • PARI
    See Links section.

A347180 Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is visible in a(n) * a(n+1).

Original entry on oeis.org

1, 10, 11, 12, 9, 21, 2, 6, 16, 7, 25, 5, 3, 13, 8, 23, 4, 26, 17, 30, 31, 14, 15, 34, 39, 24, 18, 45, 32, 41, 28, 19, 22, 33, 40, 35, 38, 36, 37, 29, 42, 20, 46, 27, 47, 52, 49, 50, 43, 48, 51, 54, 64, 44, 55, 53, 65, 56, 63, 58, 61, 60, 66, 57, 62, 59, 67, 68, 69, 72, 76, 75, 73, 79, 82, 71, 70
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Aug 21 2021

Keywords

Examples

			a(1) * a(2) =  1 * 10 =  10;
a(2) * a(3) = 10 * 11 = 110;
a(3) * a(4) = 11 * 12 = 132;
a(4) * a(5) = 12 *  9 = 108;
a(5) * a(6) =  9 * 21 = 189; etc.

Crossrefs

Cf. A333774, A347181.

Programs

  • Python
    def aupton(terms):
    alst, aset = [1], {1}
    while len(alst) < terms:
        an, target = 2, str(alst[-1])[0]
        while an in aset or target not in str(alst[-1]*an): an += 1
        alst.append(an); aset.add(an)
    return alst
print(aupton(200)) # Michael S. Branicky, Aug 21 2021
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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