A085836 -id:A085836 - cp's OEIS frontend

A085612 Triangle in which the n-th row contains n numbers (beginning with the smallest unused value) that have the same prime signature as the first entry on that row.

1, 2, 3, 4, 9, 25, 5, 7, 11, 13, 6, 10, 14, 15, 21, 8, 27, 125, 343, 1331, 2197, 12, 18, 20, 28, 44, 45, 50, 16, 81, 625, 2401, 14641, 28561, 83521, 130321, 17, 19, 23, 29, 31, 37, 41, 43, 47, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, 24, 40, 54, 56, 88, 104, 135, 136, 152

Offset: 1

Alford Arnold, Jul 04 2003

Permutation of the natural numbers when the triangle is seen flattened, inverse = A226387, see also A224401. - Reinhard Zumkeller, Jun 05 2013

			a(7) through a(10) = 5, 7, 11, 13 because 5 has not been used.
1;
2,3;
4,9,25;
5,7,11,13;
6,10,14,15,21;
8,27,125,343,1331,2197;
12,18,20,28,44,45,50;
16,81,625,2401,14641,28561,83521,130321;

Rémy Sigrist, Table of n, a(n) for n = 1..10011
Rémy Sigrist, PARI program for A085612
Index entries for sequences that are permutations of the natural numbers

Cf. A025487, A064839, A077558.
Cf. A085836.
Cf. A046523.

import Data.List ((\\))
a085612 n k = a085612_row n !! (k-1)
a085612_row n = a085612_tabf !! (n-1)
a085612_tabf = f 0 $ zip [1..] a046523_list where
   f x zs'@(z:zs) = (map fst ys) : f (x + 1) (zs' \\ ys) where
     ys = z : take x (filter ((== snd z) . snd) zs)
a085612_list = concat a085612_tabf
-- Reinhard Zumkeller, Jun 05 2013

PARI
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See Links section.
```

More terms from Ray Chandler, Aug 21 2003

A085834 Initial terms of rows in table A085612.

Original entry on oeis.org

1, 2, 4, 5, 6, 8, 12, 16, 17, 22, 24, 30, 32, 36, 48, 49, 52, 53, 57, 60, 64, 72, 96, 119, 120, 128, 139, 144, 165, 175, 180, 192, 203, 210, 216, 232, 240, 256, 283, 288, 309, 342, 360, 384, 385, 420, 432, 452, 454, 480, 512, 541, 576, 626, 663, 688, 720, 768

Offset: 1

Alford Arnold, Jul 04 2003

nonn

The least prime signature sequence (A025487) is embedded in this sequence.

Amiram Eldar, Table of n, a(n) for n = 1..141

Cf. A025487, A085612, A085836.

More terms from Amiram Eldar, Jun 28 2025

A224401 a(n) is the row number of triangle A085612 in which n appears.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 4, 6, 3, 5, 4, 7, 4, 5, 5, 8, 9, 7, 9, 7, 5, 10, 9, 11, 3, 10, 6, 7, 9, 12, 9, 13, 10, 10, 10, 14, 9, 10, 10, 11, 9, 12, 9, 7, 7, 10, 9, 15, 16, 7, 10, 17, 18, 11, 10, 11, 19, 19, 18, 20, 18, 19, 17, 21, 19, 12, 18, 17, 19, 12, 18, 22, 18, 19

Offset: 1

Matthew Goers, Apr 05 2013

nonn

Row number in A085612 triangle of prime signatures.

a(n) is not the same for all numbers n with the same prime signature. For such a sequence, see A101296. - Peter Munn, Oct 23 2023

			a(9) = 3, because 9 is in the 3rd row (1st 3 prime^2) of A085612.
a(10) = 5, because 10 is in the 5th row (1st 5 semiprimes) of A085612.
a(11) = 4, because 11 is in the 4th row (4 primes, prime(3)..prime(6)) of A085612.

Rémy Sigrist, Table of n, a(n) for n = 1..10000 (first 150 terms from Matthew Goers)
Rémy Sigrist, PARI program for A224401

Cf. A085612, A101296.

First and last positions of each number: A085834, A085836.

import Data.List (findIndex); import Data.Maybe (fromJust)
a224401 = (+ 1) . fromJust . (`findIndex` a085612_tabf) . elem
-- Reinhard Zumkeller, Jun 05 2013

PARI
```
See Links section.
```

cp's OEIS Frontend

A085612 Triangle in which the n-th row contains n numbers (beginning with the smallest unused value) that have the same prime signature as the first entry on that row.

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A085834 Initial terms of rows in table A085612.

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Extensions

A224401 a(n) is the row number of triangle A085612 in which n appears.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

PARI