

A265669


Carmichael numbers that are the average of two consecutive primes.


1



15841, 126217, 656601, 1193221, 2704801, 6189121, 8134561, 8719921, 11205601, 13992265, 40917241, 41298985, 43286881, 56052361, 76595761, 88689601, 105869401, 130497361, 167979421, 175997185, 186782401, 289766701, 367939585, 597717121, 633639097
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OFFSET

1,1


COMMENTS

Motivation was the form of differences between consecutive primes that generate this sequence. It seems that 12*k appears in all differences except 4.
Differences between corresponding consecutive primes are 36, 12, 4, 24, 24, 24, 24, 36, 24, 12, 36, 12, 36, 36, 60, 24, 36, 36, 60, 36, 24, 24, 24, 36, 12, 24 ...


LINKS

Table of n, a(n) for n=1..25.
G. Tarry, I. Franel, A. Korselt, and G. Vacca, Problème chinois, L'intermédiaire des mathématiciens 6 (1899), pp. 142144.
Eric Weisstein's World of Mathematics, Carmichael Number
Index entries for sequences related to Carmichael numbers


EXAMPLE

15841 is a term because it is a Carmichael number and average of 15823 and 15859 that are consecutive primes is equal to 15841.
126217 is a term because it is a Carmichael number and average of 126211 and 126223 that are consecutive primes is equal to 126217.


PROG

(PARI) is(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}
forcomposite(n=1, 1e9, if(is(n) && (nextprime(n)n)==(nprecprime(n)), print1(n, ", ")))


CROSSREFS

Cf. A002997.
Sequence in context: A216180 A112450 A063847 * A184612 A277350 A101320
Adjacent sequences: A265666 A265667 A265668 * A265670 A265671 A265672


KEYWORD

nonn


AUTHOR

Altug Alkan, Dec 12 2015


STATUS

approved



