This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006972 Lucas-Carmichael numbers: squarefree composite numbers n such that p | n => p+1 | n+1. (Formerly M5450) 38
 399, 935, 2015, 2915, 4991, 5719, 7055, 8855, 12719, 18095, 20705, 20999, 22847, 29315, 31535, 46079, 51359, 60059, 63503, 67199, 73535, 76751, 80189, 81719, 88559, 90287, 104663, 117215, 120581, 147455, 152279, 155819, 162687, 191807, 194327, 196559, 214199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Wright proves that this sequence is infinite (Main Theorem 2). - Charles R Greathouse IV, Nov 03 2015 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 399, p. 89, Ellipses, Paris 2008. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Paolo P. Lava and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 550 terms from Paolo P. Lava) Ed Copeland and Brady Haran, Something special about 399, Numberphile video (2015) Wikipedia, Lucas-Carmichael number Thomas Wright, There are infinitely many elliptic Carmichael numbers Thomas Wright, There are infinitely many elliptic Carmichael numbers, arXiv:1609.00231 [math.NT], (September 2016) MAPLE with(numtheory): a:= proc(n) option remember; local k; for k from 1+      `if`(n=1, 3, a(n-1)) while isprime(k) or not issqrfree(k)        or add(irem(k+1, i+1), i=factorset(k))>0 do od; k     end: seq(a(n), n=1..15);  # Alois P. Heinz, Apr 05 2018 MATHEMATICA Select[ Range[ 2, 10^6 ], !PrimeQ[ # ] && Union[ Transpose[ FactorInteger[ # ] ][ [ 2 ] ] ] == {1} && Union[ Mod[ # + 1, Transpose[ FactorInteger[ # ] ][ [ 1 ] ] + 1 ] ] == {0} & ] PROG (PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f[, 1]>1 \\ Charles R Greathouse IV, Sep 23 2012 CROSSREFS Intersection of A024556 and A056729. Cf. A216925, A216926, A216927, A217002, A217003, A217091 (terms having 3, 4, 5, 6, 7 and 8 factors). Cf. A216929. Sequence in context: A158317 A227008 A253597 * A216925 A292573 A299213 Adjacent sequences:  A006969 A006970 A006971 * A006973 A006974 A006975 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 19:33 EST 2018. Contains 318081 sequences. (Running on oeis4.)