The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000533

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A000533

a(0)=1; a(n) = 10^n + 1, n >= 1.
(history; published version)

#113 by Charles R Greathouse IV at Thu Sep 08 08:44:28 EDT 2022

PROG

(MAGMAMagma) [10^n + 1 - 0^n: n in [0..30]]; // Vincenzo Librandi, Jul 15 2011

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#112 by N. J. A. Sloane at Mon Dec 02 14:31:25 EST 2019

STATUS

proposed

approved

#111 by Jon E. Schoenfield at Tue Nov 19 23:46:28 EST 2019

STATUS

editing

proposed

#110 by Jon E. Schoenfield at Tue Nov 19 23:44:10 EST 2019

COMMENTS

Based on factors from A001271, the first abundant number in this sequence should occur in the first M terms, where M is the double factorial nM=7607!!. Is any abundant number known in this sequence? - Sergio Pimentel, Oct 04 2019

The smallest n such that a(n) is an abundant number does not exceed 3^4 5 * 5 ^2 * 7 ^2 * 11 ^2 * 13 ^2 * 17 * 19 * 23 * 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 * 73 * 79 * 83 * 89 * 97 * 101 * 103 * 107 * 109 * 113 * 127 * 131 * 137 * 139 * 157 * 163 * 181 * 191 * 241 * 251 * 263 * Product_{p prime, 3<=p<=139} p)-th term of this sequence is an abundant number. - Jon E. Schoenfield, Nov 19 2019

Discussion

Tue Nov 19

23:45

Jon E. Schoenfield: It seems good to me.  Was it okay for me to change "n=7607!!" to "M=7607!!"?  Or was that a bad idea?

23:46

Jon E. Schoenfield: I would be glad to get any advice about better ways to word my entry answering Sergio's question!

#109 by Jon E. Schoenfield at Tue Nov 19 23:39:19 EST 2019

COMMENTS

The smallest n such that a(n) is an abundant number does not exceed 3^4 * 5 * 7 * 11 * 13 * 157 * 163 * 181 * 191 * 241 * 251 * 263 * Product_{p prime, 3<=p<=139} p. - Jon E. Schoenfield, Nov 19 2019

STATUS

proposed

editing

#108 by N. J. A. Sloane at Tue Nov 19 07:12:16 EST 2019

STATUS

editing

proposed

#107 by N. J. A. Sloane at Tue Nov 19 07:11:54 EST 2019

COMMENTS

The Based on factors from A001271, the first abundant number in this sequence should occur before in the first M terms, where M is the double factorial n=7607!! based on factors from A001271. Has anybody found an Is any abundant number known in this sequence? - Sergio Pimentel, Oct 04 2019

STATUS

proposed

editing

Discussion

Tue Nov 19

07:12

N. J. A. Sloane: I rewrote the comment - OK?

#106 by Jon E. Schoenfield at Sun Nov 10 16:12:16 EST 2019

STATUS

editing

proposed

Discussion

Sun Nov 10

17:02

Jon E. Schoenfield: Or maybe I'm wrong?  Maybe the intent really is that the first abundant number should occur somewhere in the first 2.8..*10^13112 terms?

Mon Nov 11

03:55

Jon E. Schoenfield: a(n) is an abundant number at n = 
285719872123231022383152317477417882800
29261370528097979102917903430833051925
(and almost certainly at some smaller values of n as well).
The above value of n is a little larger than 97!! = 97*95*93*...*5*3*1.

17:07

Jon E. Schoenfield: @Editors -- I don't know whether the subject of the first abundant number in this sequence is of general interest.  If not, I guess this draft should be reverted.  Otherwise, if the new comment is kept, and it asks a question, I assume it'd be worthwhile to add an answer.  If so, I don't know whether it would be better to say something like

     The smallest n such that a(n) is an abundant number does not exceed 28571987212323102238315231747741788280029261370528097979102917903430833051925.

or

     The smallest n such that a(n) is an abundant number does not exceed 3^5 * 5^2 * 7^2 * 11^2 * 13^2 * 17 * 19 * 23 * 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 * 73 * 79 * 83 * 89 * 97 * 101 * 103 * 107 * 109 * 113 * 127 * 131 * 137 * 139 * 157 * 163 * 181 * 191 * 241 * 251 * 263.

or

     The smallest n such that a(n) is an abundant number does not exceed 3^4 * 5 * 7 * 11 * 13 * 157 * 163 * 181 * 191 * 241 * 251 * 263 * Product_{p prime, 3<=p<=139} p.

or something else...

#105 by Jon E. Schoenfield at Sun Nov 10 16:12:12 EST 2019

COMMENTS

It seems that the sequence gives 'all' positive integers m with such that m^4 is a palindrome. Note that a(0)^4 = 1 is a palindrome and for n > 0, a(n)^4 = (10^n + 1)^4 = 10^(4n) + 4*10^(3n) + 6*10^(2n) + 4*10^(n) + 1 is a palindrome. - Farideh Firoozbakht, Oct 28 2014

a(n)^2 starts with a(n)+1 for n >= 1. - Dhilan Lahoti, Aug 31 2015

STATUS

proposed

editing

#104 by Jon E. Schoenfield at Sun Nov 10 16:10:31 EST 2019

STATUS

editing

proposed