The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A355893 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A355893

Let A090252(n) = Product_{i >= 1} prime(i)^e(i); then a(n) is the concatenation, in reverse order, of e_1, e_2, ..., ending at the exponent of the largest prime factor of A090252(n); a(1)=0 by convention.
(history; published version)

#33 by N. J. A. Sloane at Wed Aug 24 12:01:47 EDT 2022

STATUS

editing

approved

#32 by N. J. A. Sloane at Wed Aug 24 12:01:43 EDT 2022

COMMENTS

Computed by hand, needs checking. Needs a b-file.

STATUS

reviewed

editing

#31 by Rémy Sigrist at Wed Aug 24 11:52:24 EDT 2022

STATUS

proposed

reviewed

#30 by Michael De Vlieger at Wed Aug 24 10:26:13 EDT 2022

STATUS

editing

proposed

Discussion

Wed Aug 24

10:59

Michael De Vlieger: Note: my program at A90252 is correct.

#29 by Michael De Vlieger at Wed Aug 24 10:22:14 EDT 2022

DATA

0, 1, 10, 100, 2, 1000, 20, 10000, 100000, 1000000, 3, 10000000, 100000000, 200, 1010, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 4, 10000000000000000, 4, 100000000000000000

LINKS

Michael De Vlieger, <a href="/A355893/b355893.txt">Table of n, a(n) for n = 1..1073</a>

EXAMPLE

16 ..........................1000000000

16 17 .........................10000000000

17 18 ........................100000000000

18 19 .......................1000000000000

19 20 ......................10000000000000

20 21 .....................100000000000000

21 22 ....................1000000000000000

22 ...................10000000000000000

24 ..................100000000000000000

24 ...................10000000000000000

MATHEMATICA

nn = 24, s = Import["https://oeis.org/A090252/b090252.txt", "Data"][[1 ;; nn, -1]]; f[n_] := If[n == 1, 0, Function[g, FromDigits@ Reverse@ ReplacePart[Table[0, {PrimePi[g[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, g]]@ FactorInteger@ n]; Array[f[s[[#]]] &, nn] (* Michael De Vlieger, Aug 24 2022 *)

STATUS

proposed

editing

Discussion

Wed Aug 24

10:26

Michael De Vlieger: Primes in A90252(16..24) had one too many zeros. A90252(16) = 29, pi(29) = 10, hence, A54841(A90252(16)) = 1 followed by 9 zeros, i.e., a 1 in the pi(29)-th place. Data furnished from Russ Cox's a-file at A090252. Stefano Spezia seems to have found an error in my program at A090252, I am looking into it.

#28 by N. J. A. Sloane at Wed Aug 24 09:17:09 EDT 2022

STATUS

editing

proposed

#27 by N. J. A. Sloane at Wed Aug 24 09:17:05 EDT 2022

COMMENTS

A090252 and A354169 are similar in many ways. This sequence and A355892 illustrate this.

STATUS

approved

editing

#26 by N. J. A. Sloane at Wed Aug 24 04:18:27 EDT 2022

STATUS

proposed

approved

#25 by Stefano Spezia at Wed Aug 24 02:57:31 EDT 2022

STATUS

editing

proposed

Discussion

Wed Aug 24

03:04

Stefano Spezia: I contacted Michael De Viegler asking to check his Mathematica code in A090252 which seems to be not working

#24 by Stefano Spezia at Wed Aug 24 02:56:55 EDT 2022

CROSSREFS

Cf. A054841, A090252, A354169, A090252.