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A265669 Carmichael numbers that are the average of two consecutive primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Dec 12 2015
STATUS
approved

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Last modified June 16 14:12 EDT 2024. Contains 373430 sequences. (Running on oeis4.)