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Revision History for A346431

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Primes p such that A007663(i) is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.
(history; published version)

#10 by N. J. A. Sloane at Wed Jul 21 09:34:42 EDT 2021

STATUS

proposed

approved

#9 by Felix Fröhlich at Wed Jul 21 04:57:40 EDT 2021

STATUS

editing

proposed

#8 by Felix Fröhlich at Wed Jul 21 04:56:22 EDT 2021

NAME

Primes p = prime(i) such that A007663(i) is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.

STATUS

proposed

editing

Discussion

Wed Jul 21

04:57

Felix Fröhlich: Sorry Michel. I just realized that the first part was redundant. "where i is the index of p in A000040" should be sufficient.

#7 by Michel Marcus at Wed Jul 21 04:41:01 EDT 2021

STATUS

editing

proposed

#6 by Michel Marcus at Wed Jul 21 04:40:58 EDT 2021

NAME

Primes p = pprime(i) such that A007663(i) is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.

STATUS

proposed

editing

#5 by Felix Fröhlich at Wed Jul 21 04:36:36 EDT 2021

STATUS

editing

proposed

#4 by Felix Fröhlich at Wed Jul 21 04:28:08 EDT 2021

EXAMPLE

(2^(157-1)-1)/157 is divisible by 3 * 7 * 79 * 2731 * 8191 * 121369 * 22366891, so 157 is a term of the sequence.

#3 by Felix Fröhlich at Wed Jul 21 04:20:48 EDT 2021

NAME

Primes p = p(i) such that A007663(i)/p is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.

#2 by Felix Fröhlich at Sun Jul 18 04:46:45 EDT 2021

NAME

allocated for Felix Fröhlich

Primes p = p(i) such that A007663(i)/p is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.

DATA

157, 313, 547, 859, 937, 1093, 1171, 1249, 1327, 1483, 1873, 1951, 2029, 2341, 2887, 3121, 3433, 3511, 3823, 4057, 4447, 4603, 4759, 4993, 5227, 5851, 6007, 6163, 6397, 6553, 6709, 7177, 7333, 7411, 7489, 7723, 7879, 8269, 8581, 8737, 8893, 8971, 9049, 9127

OFFSET

1,1

COMMENTS

Differs from A142159 in that 79, 2731, 8191, ... are not in this sequence.

Includes the two known Wieferich primes 1093 and 3511 (cf. A001220).

Is this a supersequence of A001220, i.e., are all Wieferich primes in the sequence?

Is p-1 always divisible by 78 = 2 * 3 * 13?

For the initial primes p in this sequence, p-1 has some interesting digit patterns in various bases, as illustrated in the following table:

p | b | base-b expansion of p-1

--------------------------------------

157 | 5 | 1111

313 | 5 | 2222

547 | 3 | 202020

547 | 4 | 20202

547 | 5 | 4141

547 | 9 | 666

547 | 16 | 222

859 | 2 | 1101011010

937 | 3 | 1021200 (nearly palindromic)

937 | 4 | 32220 (nearly palindromic)

937 | 5 | 12221

1093 | 2 | 10001000100 (periodic)

1093 | 3 | 1111110 (nearly palindromic/repdigit)

1093 | 4 | 101010

1093 | 5 | 13332 (nearly palindromic)

1093 | 16 | 444

1171 | 2 | 10010010010 (periodic)

1171 | 5 | 14140 (nearly palindromic and periodic)

1171 | 8 | 2222

1249 | 3 | 1201020 (nearly palindromic)

1249 | 5 | 14443 (nearly palindromic)

1327 | 5 | 20301 (nearly palindromic)

PROG

(PARI) fq(n) = (2^(n-1)-1)/n

my(prd=3*7*79*2731*8191*121369*22366891); forprime(p=1, , if(Mod(fq(p), prd)==0, print1(p, ", ")))

CROSSREFS

Cf. A000040, A001220, A007663, A343763.

KEYWORD

allocated

nonn

AUTHOR

Felix Fröhlich, Jul 18 2021

STATUS

approved

editing

#1 by Felix Fröhlich at Sat Jul 17 09:46:59 EDT 2021

NAME

allocated for Felix Fröhlich

KEYWORD

allocated

STATUS

approved