A222413 All primes p > 5 such that A001175(p) is smaller than the maximal value permitted by Wall's Theorems 6 and 7.

29, 47, 89, 101, 107, 113, 139, 151, 181, 199, 211, 229, 233, 263, 281, 307, 331, 347, 349, 353, 401, 421, 461, 509, 521, 541, 557, 563, 619, 661, 677, 691, 709, 743, 761, 769, 797, 809, 811, 829, 859, 881, 911, 919, 941, 953, 967, 977, 991, 1009, 1021, 1031, 1049, 1061, 1069, 1087, 1097, 1103, 1109, 1151, 1217, 1223, 1229, 1231, 1249, 1277

Offset: 1

Author

N. J. A. Sloane, Feb 28 2013

Keywords

• nonn

Comments

Included because A001175 is still a mystery (as are many sequences of the same type).

A222414 gives the corresponding values of A001175(a(n)).

The maximal value for a prime p > 5 is p-1 if p == 1 or 9 (mod 10) and 2*(p+1) if p == 3 or 7 (mod 10). See Wall's Theorems 6 and 7. These values are given in A253806. - Wolfdieter Lang, Jan 16 2015

Prime(n) is a member if and only if A296240(n) > 1. - Jonathan Sondow, Dec 10 2017

Examples

			From _Wolfdieter Lang_, Jan 16 2015: (Start)
a(1) = 29 because A001175(29) = 14 but the maximal value is 29 - 1 = 28.
a(2) = 47 because A001175(47) = 32 but the maximal value is 2*(47 + 1) = 96.
All other primes p > 5 have A001175(p) = maximal value for p.
E.g., p = 11 has  A001175(11) = 11-1 = 10 and  p = 7 has A001175(7) = 2*(7 + 1) = 16. (End)
		

Links

• D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.

Crossrefs

Cf. A001175, A060305, A222414, A296240.

Cf. A001176, A001177. - Wolfdieter Lang, Jan 16 2015

Extensions

Name corrected by Wolfdieter Lang, Jan 16 2015