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A290692
Carmichael numbers of the form p - 2 where p is a prime number.
2
561, 2465, 656601, 1909001, 174352641, 230996949, 275283401, 939947009, 1534274841, 3264820001, 5860426881, 6025532241, 25536531021, 36709177121, 53388707681, 54519328481, 56222911361, 101536702401, 105528976961, 180481509681, 196866607601, 239862350001, 329245587161, 347469383801, 347511324161
OFFSET
1,1
COMMENTS
Rotkiewicz mentioned the first six terms of this sequence at the end of page 59 of his article (Links section). But his list includes 2821 and 46657 (2823 = 3 * 941 and 46659 = 3 * 103 * 151), which should not be there.
Carmichael numbers of the form p + 2 where p is a prime number are 1105, 2821, 6601, 29341, 41041, 52633, ... (see also A272754 for corresponding prime numbers).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..5901 (terms below 10^22 calculated using data from Claude Goutier; terms 1..591 from Robert Israel)
R. G. E. Pinch, Carmichael numbers up to 10^16, 10^16 to 10^17, 10^17 to 10^18
Andrzej Rotkiewicz, On pseudoprimes having special forms and a solution of K. Szymiczek's problem, Acta Mathematica Universitatis Ostraviensis, Vol. 13, No. 1 (2005), pp. 57-71.
MAPLE
# Using data file from Richard Pinch
infile:= "carmichael-16": Res:= NULL;
do
S:= readline(infile);
if S = 0 then break fi;
L:= sscanf(S, "%d");
if nops(L) <> 1 then break fi;
if isprime(L[1]+2) then Res:= Res, L[1]; fi
od:
Res; # Robert Israel, Jun 03 2019
MATHEMATICA
Cases[Range[1, 10^7, 2], n_ /; And[Mod[n, CarmichaelLambda@ n] == 1, ! PrimeQ@ n, PrimeQ[n + 2]]] (* Michael De Vlieger, Aug 09 2017, after Artur Jasinski at A002997 *)
PROG
(PARI) isA002997(n) = {my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1}
isok(n) = isprime(n+2) && isA002997(n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Aug 09 2017
EXTENSIONS
More terms from Robert Israel, Jun 03 2019
STATUS
approved