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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 (list; graph; refs; listen; history; text; internal format)
 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) Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22. 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. Index entries for sequences related to Carmichael numbers. 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 Cf. A002997, A272754, A287591. Sequence in context: A097130 A110889 A205947 * A293622 A322130 A354609 Adjacent sequences: A290689 A290690 A290691 * A290693 A290694 A290695 KEYWORD nonn AUTHOR Altug Alkan, Aug 09 2017 EXTENSIONS More terms from Robert Israel, Jun 03 2019 STATUS approved

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Last modified May 18 16:32 EDT 2024. Contains 372664 sequences. (Running on oeis4.)