A252812 Primes whose trajectories under the map x -> A039951(x) enter the cycle {83, 4871} (conjectured).

83, 4871, 8179, 11423, 14071, 16411, 29191, 29531, 35267, 41603, 47963, 56747, 58963, 61331, 68791, 68891, 76039, 82267, 94811, 96739, 110063, 122027, 124823, 156631, 175939, 179383, 183091, 188563, 192991, 198491, 206939, 216119, 219523, 231871, 232591

Offset: 1

Author

Felix Fröhlich, Dec 22 2014

Keywords

• nonn
• hard

Comments

This sequence may contain gaps, as there are some prime bases for which no Wieferich primes are known. Those bases are 47, 139, 311, 347, 983, .... (see Fischer link).

Any prime whose trajectory leads to a prime in this sequence is also a term of the sequence. Therefore, if the trajectory of any of the bases mentioned in the previous comment leads to a term in the sequence, then that base and any prime bases where it is the smallest Wieferich prime are also terms. - Felix Fröhlich, Mar 25 2015

Examples

			The trajectory of 8179 under the given map starts 8179, 83, 4871, 83, 4871, ..., entering the given cycle, so 8179 is a term of the sequence.
		

Links

• R. Fischer, Thema: Fermatquotient B^(P-1) == 1 (mod P^2)

Crossrefs

Cf. A039951, A244550, A252801, A252802.

Extensions

More terms via computing prime bases with smallest Wieferich prime 83 from Felix Fröhlich, Mar 25 2015

Name edited by Felix Fröhlich, Jun 19 2021