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.

Previous Showing 21-27 of 27 results.

A048462 Odd numbers in sorted order from generation 2 onwards.

Original entry on oeis.org

3, 7, 13, 23, 43, 67, 97, 125, 127, 179, 181, 237, 339, 403, 453, 729, 757, 879, 1109, 1399, 2199, 2653, 4491, 5335, 6231, 7461, 8933, 12093, 12613, 14409, 14687, 18183, 18917, 23591, 25131, 27933, 29199, 32877, 36233, 36639, 36949, 49193, 50745
Offset: 0

Views

Author

Patrick De Geest, May 15 1999

Keywords

Crossrefs

Cf. A048448-A048455. See also A047844.

A048463 Smallest prime occurring in generation n (0 if none).

Original entry on oeis.org

2, 3, 7, 13, 97, 127, 127, 757, 0, 8933, 0, 18917, 49193, 53831, 71023, 71023, 0, 0, 17427659, 30196487, 0, 0, 0, 0, 1586875049, 988142237, 7021048691, 1397537747, 0, 2760703019, 2760703019, 0, 0, 1033545746063, 0, 0, 7916712387631, 0, 0, 0
Offset: 0

Views

Author

Patrick De Geest, May 15 1999

Keywords

Crossrefs

For "Generations" see A048448-A048455. See also A047844.

A048464 Indices of primefree generations.

Original entry on oeis.org

9, 11, 17, 18, 21, 22, 23, 24, 29, 32, 33, 35, 36, 38, 39, 40, 48, 49, 50, 54, 56, 57, 58, 65, 66, 67, 69, 70, 72, 74, 76, 77, 78, 79, 81, 83, 85, 86, 88, 89, 91, 93, 95, 96, 97, 99, 100, 101, 106, 107, 108, 110, 111, 113, 114, 115, 121, 125, 126, 128, 129
Offset: 1

Views

Author

Patrick De Geest, May 15 1999

Keywords

Crossrefs

For "Generations" see A048448-A048455. See also A047844.

Extensions

More terms from Sean A. Irvine, Jun 18 2021

A048465 Distinct primes in sorted order from generation 2 onwards.

Original entry on oeis.org

3, 7, 13, 23, 43, 67, 97, 127, 179, 181, 757, 1109, 1399, 8933, 12613, 18917, 49193, 53831, 71023, 199909, 221317, 408379, 821771, 1330519, 17427659, 30196487, 988142237, 1397537747, 1586875049, 2760703019, 4128019327, 7021048691
Offset: 1

Views

Author

Patrick De Geest, May 15 1999

Keywords

Crossrefs

For "Generations" see A048448-A048455. See also A047844.

A084856 Prime(n+2)^2-prime(n)^2.

Original entry on oeis.org

21, 40, 96, 120, 168, 192, 240, 480, 432, 528, 720, 480, 528, 960, 1272, 912, 1008, 1320, 840, 1200, 1560, 1680, 2520, 2280, 1200, 1248, 1272, 1320, 4248, 4392, 2640, 2160, 3432, 3480, 2448, 3768, 3240, 3360, 4152, 2832, 4440, 4488, 2328, 2352, 5712
Offset: 1

Views

Author

Meir Avshalomi (amomy(AT)yahoo.com), Jul 13 2003

Keywords

Examples

			a(3)=prime(5)^2-prime(3)^2= 11^2-5^2=96

Programs

  • Mathematica
    Table[ Prime[n + 2]^2 - Prime[n]^2, {n, 1, 45}]

Formula

A031131(n)*A048448(n).

Extensions

Edited and extended by Robert G. Wilson v, Jul 19 2003

A176099 Prime(n) + A158611(n).

Original entry on oeis.org

2, 4, 7, 10, 16, 20, 28, 32, 40, 48, 54, 66, 72, 80, 88, 96, 106, 114, 126, 132, 140, 150, 156, 168, 180, 190, 200, 208, 212, 220, 236, 244, 264, 270, 286, 290, 306, 314, 324, 336, 346, 354, 370, 374, 388, 392, 408, 422, 438, 452, 460, 468, 474, 490, 498, 514
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 08 2010

Keywords

Examples

			a(2)= A000040(2)+A158611(2) = 3+1 = 4.

Crossrefs

Cf. A000040, A048448, A158611.

Formula

A048448(n) = a(n) if n <> 2.

Extensions

Entries checked by R. J. Mathar, Apr 16 2010

A357679 a(n) = prime(n)*(prime(n-1) + prime(n+1)).

Original entry on oeis.org

21, 50, 112, 220, 364, 544, 760, 1104, 1566, 2046, 2664, 3280, 3784, 4512, 5618, 6726, 7686, 8844, 9940, 10950, 12324, 13944, 16020, 18430, 20200, 21424, 22684, 23980, 26668, 30988, 34584, 36990, 39754, 43210, 46206, 49298, 52812, 56112, 59858, 63366, 66970, 71434, 74884, 77224, 81192
Offset: 2

Views

Author

Saish S. Kambali, Oct 09 2022

Keywords

Comments

21 is the only semiprime term.
All terms after 21 are even.

Crossrefs

Cf. A000040, A048448, A006094.
Cf. A338529 (first differences).

Programs

  • Mathematica
    Array[Prime[# + 1] (Prime[#] + Prime[# + 2]) &, 45] (* Michael De Vlieger, Oct 09 2022 *)
  • PARI
    a(n) = prime(n)*(prime(n-1) + prime(n+1)) \\ Michel Marcus, Oct 09 2022

Formula

a(n) = A000040(n)*A048448(n).
a(n) = A006094(n) + A006094(n-1).
Previous Showing 21-27 of 27 results.

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