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 1-3 of 3 results.

A001748 a(n) = 3 * prime(n).

Original entry on oeis.org

6, 9, 15, 21, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723, 753
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

Semiprimes divisible by 3. - Jianing Song, Oct 02 2022

Links

Crossrefs

Subsequence of A001358.
Cf. A000040, A100484, A253046, A164023, A164024, A179545, A253046.

Programs

Formula

A164023(a(n)) = A164024(a(n)) = A000040(n). - Reinhard Zumkeller, Aug 09 2009
a(n) = 3*A000040(n). - Omar E. Pol, Jan 31 2012
A253046(a(n)) < a(n). - Reinhard Zumkeller, Dec 26 2014

A164023 Smallest of largest parts in partitions of n into exactly three primes.

Original entry on oeis.org

2, 3, 3, 3, 5, 5, 5, 5, 7, 5, 7, 7, 11, 7, 11, 7, 13, 11, 11, 11, 13, 11, 13, 11, 17, 13, 17, 11, 19, 13, 17, 13, 19, 13, 19, 17, 23, 17, 23, 17, 31, 17, 23, 19, 29, 17, 31, 19, 29, 19, 31, 19, 37, 23, 29, 23, 31, 23, 31, 23, 41, 29, 37, 23, 37, 29, 41, 31, 41, 29, 37, 29, 47, 31
Offset: 6

Views

Author

Reinhard Zumkeller, Aug 08 2009

Keywords

Comments

a(n) >= floor(n/3); a(A001748(n)) = A000040(n).

Examples

			a(16) = min{max(2,3,11),max(2,7,7)} = min{11,7} = 7;
a(17) = min{max(2,2,13),max(2,3,11),max(3,7,7),max(5,5,7)} = min{13,11,7,7} = 7.

Links

Crossrefs

A164024, A068307.

A355250 Largest prime appearing among the "middle parts" of the partitions of n into (exactly) 3 prime parts.

Original entry on oeis.org

2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 11, 13, 13, 13, 13, 13, 17, 17, 17, 17, 19, 19, 17, 19, 19, 19, 13, 19, 23, 23, 19, 23, 19, 23, 23, 23, 23, 23, 19, 23, 29, 29, 29, 29, 31, 31, 23, 31, 29, 31, 31, 31, 29, 31, 31, 31, 37, 37, 29, 37
Offset: 6

Views

Author

Wesley Ivan Hurt, Jun 25 2022

Keywords

Examples

			a(17) = 7; of the 4 ways to write 17 as the sum of 3 primes, 7 is the largest "middle" part: 2+2+13 = 3+3+11 = 3+7+7 = 5+5+7.

Links

Crossrefs

Cf. A164024.

Programs

  • Mathematica
    Table[Max[Select[IntegerPartitions[n,{3}],AllTrue[#,PrimeQ]&][[;;,2]]],{n,6,90}] (* Harvey P. Dale, Jan 31 2025 *)
Showing 1-3 of 3 results.

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

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