A133813 Numbers that are primally tight and have strictly descending powers.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 24, 25, 27, 29, 31, 32, 37, 41, 43, 45, 47, 48, 49, 53, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 96, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 135, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 175

Offset

1,2

Comments

All numbers of the form p_1^k1*p_2^k2*...*p_n^k_n, where k1 > k2 > ... > k_n and the p_i are n successive primes.

Subset of A073491, A133812.

Differs from A085233 starting n=22.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A049084(A027748(a(n),k+1)) = A049084(A027748(a(n),k)) + 1 and A124010(a(n),k+1) < A124010(a(n),k), 1 <= k < A001221(a(n)). - Reinhard Zumkeller, Apr 14 2015

Prog

(Haskell)
import Data.List (isPrefixOf)
a133813 n = a133813_list !! (n-1)
a133813_list = 1 : filter f [2..] where
   f x = isPrefixOf ps (dropWhile (< a020639 x) a000040_list) &&
           all (< 0) (zipWith (-) (tail es) es)
         where ps = a027748_row x; es = a124010_row x
-- Reinhard Zumkeller, Apr 14 2015

Crossrefs

Cf. A025487, A087980, A073491, A133808-A133812.

Cf. A027748, A124010, A049084, A020639, A000040, A087980.

Sequence in context: A354921 A085233 A357861 * A326836 A326841 A274222

Adjacent sequences: A133810 A133811 A133812 * A133814 A133815 A133816

Keyword

nonn

Author

Olivier Gérard, Sep 23, 2007

Status

approved