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A290947 Primes p1 > 3, such that p2 = 3p1-2 and p3 = (p1*p2+1)/2 are also primes, so p1*p2*p3 is a triangular 3-Carmichael number. 2
7, 13, 37, 43, 61, 193, 211, 271, 307, 331, 601, 673, 727, 757, 823, 1063, 1297, 1447, 1597, 1621, 1657, 1693, 2113, 2281, 2347, 2437, 2503, 3001, 3067, 3271, 3733, 4093, 4201, 4957, 5581, 6073, 6607, 7321, 7333, 7723, 7867, 8287, 8581, 8647, 9643, 10243 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The primes are of the form p1=(6k+1), p2=(18k+1), and p3=(54k^2+12k+1), with k = 1, 2, 6, 7, 10, 32, 35, 45, 51, 55, 100, ...

The generated triangular 3-Carmichael numbers are: 8911, 115921, 8134561, 14913991, 60957361, 6200691841, 8863329511, 24151953871, 39799655911, 53799052231, 585796503601, ...

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

p1 = 7 is in the sequence since with p2 = 3*7-2 = 19 and p3 = (7*19+1)/2 = 67 they are all primes. 7*19*67 = 8911 is a triangular 3-Carmichael number.

MATHEMATICA

seq = {}; Do[p1 = 6 k + 1; p2 = 3 p1 - 2; p3 = (p1*p2 + 1)/2;

If[AllTrue[{p1, p2, p3}, PrimeQ], AppendTo[seq, p1]], {k, 1,

  2000}]; seq

PROG

(PARI) list(lim)=my(v=List()); forprime(p=7, lim, if(isprime(3*p-2) && isprime((p*(3*p-2)+1)/2), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Aug 14 2017

CROSSREFS

Cf. A000217, A002997, A087788, A290945.

Sequence in context: A117706 A066673 A307762 * A267985 A173230 A155036

Adjacent sequences:  A290944 A290945 A290946 * A290948 A290949 A290950

KEYWORD

nonn

AUTHOR

Amiram Eldar, Aug 14 2017

STATUS

approved

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Last modified August 1 03:52 EDT 2021. Contains 346384 sequences. (Running on oeis4.)