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Revision History for A339736 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

Numbers which, in every base B, either have a digit 0, do not have a digit B-1, or only have one digit.
(history; published version)

#53 by OEIS Server at Fri Sep 17 13:16:39 EDT 2021

LINKS

Michael S. Branicky, <a href="/A339736/b339736_1.txt">Table of n, a(n) for n = 1..456</a>

#52 by Charles R Greathouse IV at Fri Sep 17 13:16:39 EDT 2021

STATUS

editing

approved

Discussion

Fri Sep 17

13:16

OEIS Server: Installed new b-file as b339736.txt.  Old b-file is now b339736_1.txt.

#51 by Charles R Greathouse IV at Fri Sep 17 13:15:05 EDT 2021

PROG

(PARI) bad(n, b)=my(d=Set(digits(n, b))); b-d[#d]==1 && d[1];

ok(n, L)=for(b=2, L, if(bad(n, b), return(0))); 1;

list(lim)=my(v=List([1])); forprime(p=3, lim+1, if(ok(p-1, sqrtint(p)+1), listput(v, p-1))); Vec(v) \\ Charles R Greathouse IV, Sep 17 2021

STATUS

proposed

editing

#50 by Michael S. Branicky at Thu Sep 16 12:30:41 EDT 2021

STATUS

editing

proposed

Discussion

Thu Sep 16

12:32

Michael S. Branicky: Done.  Was able to go much higher in value (though not a huge extra # of terms)

#49 by Michael S. Branicky at Thu Sep 16 12:29:36 EDT 2021

LINKS

Michael S. Branicky, <a href="/A339736/b339736_1.txt">Table of n, a(n) for n = 1..429456</a>

STATUS

proposed

editing

Discussion

Thu Sep 16

12:30

Michael S. Branicky: Done.  Was able to go much higher in value (though not a huge extra # of terms)

#48 by Alex Stefanov at Mon Sep 13 08:34:01 EDT 2021

STATUS

editing

proposed

Discussion

Mon Sep 13

08:46

Kevin Ryde: Could say the digits outright if it helped.  Umm m+1 = b*q means that m = (q-1)*b + b-1 which is digits q-1,b-1.

08:51

Kevin Ryde: m+1 prime should be good in program code too.  With that, think bases b testing can stop when reach 2-digits of which the high is < b-1, since no bigger b will go bad.  Does that sound right?  The stop would be near sqrt(m), but watching for the high digit may be easier.

Tue Sep 14

09:18

Michael S. Branicky: Good ideas, Kevin.  In practice, filtering only primes helps speed at start (1.5x to 200) but not as terms grow bigger, since the time is dominated by merely checking the correct ones.

09:23

Michael S. Branicky: I tried the two-digit cutoff as well.  I got errors checking "2-digits of which the high is < b-1".  I think the stopping condition is when you reach something less than (1, b-1).  I am trying a run with that.

19:55

Kevin Ryde: Hmm.  2-digits condition depends on m+1 being prime.  Think it's right together with that.  Bit of unsophisticated pari for definiteness:

is(m) = if(m==1,return(1)); isprime(m+1) || return(0); for(b=2,m, my(v=digits(m,b)); if(#v<=2 && v[1]<b-1,break); if(vecmin(v)!=0 && vecmax(v)==b-1, return(0))); 1;

#47 by Alex Stefanov at Mon Sep 13 08:32:18 EDT 2021

COMMENTS

Every term is 1 less than a prime number because, for all numbers m and m+1, , if m+1 is not prime then, in base b = largest divisor of m+1, m+1 is a two digit number ending in 0 and b-1 (since m +1 is a two digit number ending in b-1, 0), thus proving m is not in the sequence. (End)

STATUS

proposed

editing

#46 by Michel Marcus at Mon Sep 13 07:44:47 EDT 2021

STATUS

editing

proposed

Discussion

Mon Sep 13

08:25

Kevin Ryde: Yes on that m+1 prime.  (And yes fine to be yours :)  I think omit "m+1 is a two digit number ending in 0" since it's the digits of m are the relevant test (if I understood!).

08:28

Alex Stefanov: m+1 ending in 0 is not relevant in the test but I included it to make it easier to see why m contains b-1

#45 by Michel Marcus at Mon Sep 13 07:44:00 EDT 2021

COMMENTS

From Alex Stefanov, Sep 13 2021: (Start)

Every term is 1 less than a prime number because, for all numbers m and m+1, if m+1 is not prime then, in base b = largest divisor of m+1, m+1 is a two digit number ending in 0 and m is a two digit number ending in b-1, thus proving m is not in the sequence. - _Alex Stefanov_, Sep 13 2021(End)

STATUS

proposed

editing

Discussion

Mon Sep 13

07:44

Michel Marcus: yes; to understand my edit, see https://oeis.org/wiki/Style_Sheet#Signing_your_name_when_you_contribute_to_an_existing_sequence

#44 by Giorgos Kalogeropoulos at Mon Sep 13 06:25:37 EDT 2021

STATUS

editing

proposed