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A272754 Primes p such that p + 2 is a Carmichael number (A002997). 2
1103, 2819, 6599, 29339, 41039, 52631, 62743, 172079, 188459, 278543, 340559, 488879, 656599, 670031, 1033667, 2100899, 3146219, 5048999, 6049679, 8719307, 10024559, 10402559, 10877579, 11119103, 12261059, 14913989, 15247619, 15829631, 15888311, 17315999, 17812079, 18900971, 25603199, 26921087 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Because of Korselt's criterion, prime p is a member of this sequence if and only if p+2 is composite squarefree and q-1 divides p+1 for every prime q dividing p+2.

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

1103 is a term because 1103 is prime and 1105 is a Carmichael number.

MATHEMATICA

Select[Cases[Range[1, 10^7, 2], n_ /; Mod[n, CarmichaelLambda[n]] == 1 && ! PrimeQ[n]] - 2, PrimeQ] (* Michael De Vlieger, May 05 2016, 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}

lista(nn) = forprime(p=2, nn, if(isA002997(p+2), print1(p, ", ")));

CROSSREFS

Cf. A002997, A135437.

Sequence in context: A178348 A250796 A271431 * A060519 A197422 A291134

Adjacent sequences:  A272751 A272752 A272753 * A272755 A272756 A272757

KEYWORD

nonn

AUTHOR

Altug Alkan, May 05 2016

STATUS

approved

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Last modified May 21 00:41 EDT 2019. Contains 323427 sequences. (Running on oeis4.)