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A222413 All primes p > 5 such that A001175(p) is smaller than the maximal value permitted by Wall's Theorems 6 and 7. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 5 09:06 EDT 2020. Contains 334829 sequences. (Running on oeis4.)