A343763 -id:A343763 - cp's OEIS frontend

A346431 Primes p such that A007663(i) is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.

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

Felix Fröhlich, Jul 18 2021

nonn

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
--------------------------------------
|  5 | 1111
|  5 | 2222
|  3 | 202020
|  4 | 20202
|  5 | 4141
|  9 | 666
| 16 | 222
|  2 | 1101011010
|  3 | 1021200 (nearly palindromic)
|  4 | 32220 (nearly palindromic)
|  5 | 12221
|  2 | 10001000100 (periodic)
|  3 | 1111110 (nearly palindromic/repdigit)
|  4 | 101010
|  5 | 13332 (nearly palindromic)
| 16 | 444
|  2 | 10010010010 (periodic)
|  5 | 14140 (nearly palindromic and periodic)
|  8 | 2222
|  3 | 1201020 (nearly palindromic)
|  5 | 14443 (nearly palindromic)
|  5 | 20301 (nearly palindromic)

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

Cf. A000040, A001220, A007663, A343763.

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, ", ")))

cp's OEIS Frontend

A346431 Primes p such that A007663(i) is divisible by Product_{k=1..7} A343763(k), where i is the index of p in A000040.

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