A265669 Carmichael numbers that are the average of two consecutive primes.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

G. Tarry, I. Franel, A. Korselt, and G. Vacca, Problème chinois, L'intermédiaire des mathématiciens 6 (1899), pp. 142-144.

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)==(n-precprime(n)), print1(n, ", ")))

Crossrefs

Cf. A002997.

Sequence in context: A112450 A063847 A367231 * A356866 A184612 A277350

Adjacent sequences: A265666 A265667 A265668 * A265670 A265671 A265672

Keyword

nonn

Author

Altug Alkan, Dec 12 2015

Status

approved