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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A342187 Numbers k such that both k and k+1 are not exponentially odd numbers.

Original entry on oeis.org

44, 48, 49, 63, 75, 80, 98, 99, 116, 147, 171, 175, 207, 244, 260, 275, 288, 315, 324, 332, 360, 363, 368, 387, 404, 475, 476, 495, 507, 524, 528, 531, 539, 548, 549, 575, 603, 604, 624, 636, 656, 675, 692, 724, 725, 747, 764, 774, 800, 819, 832, 844, 845, 846
Offset: 1

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Author

Amiram Eldar, Mar 04 2021

Keywords

Comments

The numbers of terms not exceeding 10^k for k = 2, 3, ..., are 8, 64, 624, 6281, 62779, 627904, 6279725, 62796307, 627961560, ... Apparently this sequence has an asymptotic density 0.062796...

Examples

			44 is a term since 44 = 2^2 * 11 and 45 = 3^2 * 5 both have an even exponent in their prime factorization.

Links

Crossrefs

Cf. A072587, A268335.
Similar sequences: A068140, A068781, A342188, A342189.

Programs

  • Mathematica
    expOddQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], OddQ]; Select[Range[10^3], !expOddQ[#] && !expOddQ[# + 1] &]

A342189 Numbers k such that both k and k+1 are not exponentially 2^n-numbers.

Original entry on oeis.org

135, 296, 343, 351, 375, 512, 728, 999, 1160, 1215, 1375, 1431, 1592, 1624, 2079, 2240, 2295, 2375, 2456, 2624, 2727, 2888, 2943, 3104, 3159, 3429, 3591, 3624, 3752, 3992, 4023, 4184, 4616, 4671, 4832, 4887, 4913, 5048, 5144, 5319, 5480, 5535, 5696, 5831, 6183
Offset: 1

Views

Author

Amiram Eldar, Mar 04 2021

Keywords

Comments

The numbers of terms not exceeding 10^k for k = 3, 4, ..., are 8, 76, 775, 7776, 77845, 778303, 7783285, 77832769, ... Apparently this sequence has an asymptotic density 0.0077832...

Examples

			135 is a term since 135 = 3^3 * 5 and 136 = 2^3 * 17 both have an exponent in their prime factorization which is not a power of 2.

Links

Crossrefs

cf. A138302.
Similar sequences: A068140, A068781, A342187, A342188.

Programs

  • Mathematica
    exp2nQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], # == 2^IntegerExponent[#, 2] &]; Select[Range[10^4], ! exp2nQ[#] && ! exp2nQ[# + 1] &]
Showing 1-2 of 2 results.

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

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