login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k such that Fibonacci(k) == +-1 (mod k) and k is neither 1 nor prime nor twice a prime.
2

%I #6 May 06 2017 05:55:28

%S 323,572,646,754,2737,3782,4181,5474,5777,6479,6721,7654,7743,8362,

%T 10877,11554,11663,12958,13201,13202,13442,15251,16298,17261,17302,

%U 18407,19043,21754,23042,23326,23407,26402,26978,27071,27962,30502,34238,34561,34943,35207

%N Numbers k such that Fibonacci(k) == +-1 (mod k) and k is neither 1 nor prime nor twice a prime.

%C Included among the 313 terms less than 10^6 in this sequence are 70 semiprimes, among which are 9 twin prime products (323=17*19, 11663=107*109, 19043=137*139, 39203=197*199, 51983=227*229, 121103=347*349, 381923=617*619, 685583=827*829, 736163=857*859), 8 of the form p(2p+3) (5777=53*109, 10877=73*149, 75077=193*389, 100127=223*449, 161027=283*569, 430127=463*929, 635627=563*1129), and 4 of the form p(3p-2) (97921=181*541, 556421=431*1291, 636641=461*1381, 722261=491*1471).

%H Giovanni Resta, <a href="/A279072/b279072.txt">Table of n, a(n) for n = 1..10000</a>

%e 323 is in the sequence because Fibonacci(323) mod 323 = 1.

%e 646 (=2*323) is in the sequence because Fibonacci(646) mod 646 = 645 and 645 == -1 (mod 646).

%Y Cf. A000045, A279071.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Dec 30 2016