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A182207 Carmichael numbers of the form C = p*(2p-1)*(n*(2p-2)+p), where p and 2p-1 are prime numbers. 0
1729, 2821, 41041, 63973, 101101, 126217, 172081, 188461, 294409, 399001, 488881, 512461, 670033, 748657, 838201, 852841, 997633, 1033669, 1050985, 1082809, 1461241, 2100901, 2113921, 2628073, 4463641, 4909177, 7995169, 8341201, 8719309, 9890881 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: Any Carmichael number C divisible by p and 2p-1 (where p and 2p-1 are prime numbers) can be written as C = p*(2p-1)*(n*(2p-2)+p).

Checked for the first 30 Carmichael numbers divisible by p and 2p-1.

Note: we can see how easy is to obtain Carmichael numbers with this formula:

for n = 1 we get p*(2p-1)*(3p-2) and Carmichael numbers 1729, 172081, 294409 etc.

for n = 2 we get p*(2p-1)*(5p-4) and Carmichael numbers 2821, 63973, 488881 etc.

for n = 3 we get p*(2p-1)*(7p-6) and Carmichael numbers 399001, 53711113 etc.

LINKS

Table of n, a(n) for n=1..30.

E. W. Weisstein, Carmichael Number

PROG

(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1

list(lim)=my(v=List(), q, t); forprime(p=3, round(solve(x=1, lim, 6*x^3-7*x^2+2*x-lim)), for(n=1, (lim\(2*p^2-p)-p)\(2*p-2), if(isprime(q=2*p-1)&&Korselt(t=p*q*(n*q-n+p)), listput(v, t)))); vecsort(Vec(v), , 8)

\\ Charles R Greathouse IV, Oct 02 2012

CROSSREFS

Sequence in context: A083737 A182208 A324316 * A138129 A242880 A001235

Adjacent sequences:  A182204 A182205 A182206 * A182208 A182209 A182210

KEYWORD

nonn

AUTHOR

Marius Coman, Apr 18 2012

STATUS

approved

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Last modified February 19 00:57 EST 2020. Contains 332028 sequences. (Running on oeis4.)