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

1,1

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

Links

Table of n, a(n) for n=1..66.

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

Example

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)

Crossrefs

Cf. A001175, A060305, A222414, A296240.

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

Sequence in context: A138052 A119891 A106754 * A063642 A108258 A232236

Adjacent sequences: A222410 A222411 A222412 * A222414 A222415 A222416

Keyword

nonn

Author

N. J. A. Sloane, Feb 28 2013

Extensions

Name corrected by Wolfdieter Lang, Jan 16 2015

Status

approved