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.

A357986 a(n) is the unique k such that A357579(k) = A007916(n), or -1 if no such k exists.

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Oct 23 2022

Keywords

Examples

			A357579(36) = 42 = A007916(33), so a(33) = 36.

Links

Crossrefs

Cf. A007916, A357579.

Programs

  • PARI
    See Links section.

A357988 a(n) is the unique k such that A357579(k) = prime(n) (the n-th prime number), or -1 if no such k exists.

Original entry on oeis.org

1, 2, 4, 3, 8, 12, 9, 16, 15, 21, 26, 24, 30, 34, 43, 40, 45, 47, 53, 67, 59, 64, 70, 74, 84, 94, 89, 96, 93, 107, 110, 112, 120, 128, 124, 134, 137, 148, 156, 150, 163, 161, 170, 174, 180, 186, 189, 208, 201, 209, 213, 207, 222, 219, 240, 244, 245, 247, 250
Offset: 1

Views

Author

Rémy Sigrist, Oct 23 2022

Keywords

Examples

			A357579(53) = 67 = prime(19), so a(19) = 53.

Links

Crossrefs

Cf. A357579, A357986.

Programs

  • C
    See Links section.
  • PARI
    See Links section.

Formula

a(n) = A357986(prime(n)).

A357987 Lexicographically earliest sequence of positive integers such that no sum of consecutive terms is a square or higher power of an integer.

Original entry on oeis.org

2, 3, 2, 5, 5, 2, 3, 2, 21, 5, 2, 5, 5, 5, 7, 6, 5, 6, 6, 7, 11, 24, 2, 13, 5, 6, 35, 7, 10, 34, 6, 15, 2, 28, 10, 2, 5, 14, 19, 2, 5, 28, 2, 3, 2, 35, 2, 18, 6, 11, 3, 3, 37, 2, 5, 26, 29, 33, 42, 13, 5, 5, 10, 11, 13, 21, 18, 5, 10, 5, 6, 7, 24, 20, 3, 15
Offset: 1

Views

Author

Rémy Sigrist, Oct 23 2022

Keywords

Comments

This sequence is a variant of A357579 where we allow duplicates.
This sequence is well defined as we have arbitrary large gaps in A001597.

Examples

			For n = 1:
- 2 is not a perfect power,
- so a(1) = 2.
For n = 2:
- 2 + 2 is a perfect power,
- neither 2 + 3 nor 3 are perfect powers,
- so a(2) = 3.
For n = 3:
- none of 2 + 3 + 2, 3 + 2, 2 is a perfect power,
- so a(3) = 2.

Links

Crossrefs

Cf. A001597, A007916, A357579.

Programs

  • C
    See Links section.

A357989 Lexicographically earliest sequence of distinct numbers such that every sum of consecutive terms is an evil number (A001969).

Original entry on oeis.org

0, 3, 6, 9, 15, 24, 29, 43, 58, 53, 18, 68, 298, 399, 71, 373, 2628, 444, 768, 2304, 6144, 2631, 441, 3072, 1604, 10684, 33348, 1212, 3908, 11452, 836, 3075, 1209, 43264, 98304, 33351, 3513, 1607, 10681, 1675, 3001, 44476, 4676, 12288, 3516, 176128, 524868
Offset: 1

Views

Author

Rémy Sigrist, Oct 23 2022

Keywords

Comments

This sequence has similarities with A357579; here we avoid odious numbers, there we avoid perfect powers.
This sequence is well defined as we can always extend the sequence with an evil number whose binary expansion has no 1's in common with all sums of consecutive terms so far.

Examples

			For n = 1:
- 0 is evil,
- so a(1) = 0.
For n = 2:
- 1 and 2 are odious,
- 0 + 3 and 3 are evil,
- so a(2) = 3.
- For n = 3:
- 4 is odious,
- 3 + 5 is odious,
- 0 + 3 + 6, 3 + 6 and 6 are evil,
- so a(3) = 6.

Links

Crossrefs

Cf. A000069, A001969, A357579.
Showing 1-4 of 4 results.

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

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