A057822 Smaller of pair of twin primes whose average is lcm(1,...,m) for some m.

5, 11, 59, 419, 232792559, 442720643463713815199

Offset

1,1

Comments

Known values of m such that lcm(1,...,m) is a twin prime mean value are as follows: {3, 4, 5, 6, 7, 19, 20, 21, 22, 47, 48}.

No more such primes occurs below m < 2000.

No more such primes occurs below m < 30000. - Amiram Eldar, Aug 18 2024

Links

Table of n, a(n) for n=1..6.

Example

419 and 421 are twin primes, (419 + 421)/2 = 420 = lcm(1,2,3,4,5,6,7).

Mathematica

Select[FoldList[LCM, Select[Range[50], PrimePowerQ]] - 1, And @@ PrimeQ[# + {0, 2}] &] (* Amiram Eldar, Aug 18 2024 *)

Prog

(PARI) lista(nn=50) = {for (i=1, nn, if (isprimepower(i), if (isprime(p=lcm([2..i])-1) && isprime(p+2), print1(p, ", ")); ); ); } \\ Michel Marcus, Aug 25 2019

Crossrefs

Intersection of A057824 and {A049536(n)-2}.

Cf. A003418, A051451, A057706.

Sequence in context: A136669 A208768 A057824 * A168243 A173875 A095150

Adjacent sequences: A057819 A057820 A057821 * A057823 A057824 A057825

Keyword

nonn,hard

Author

Labos Elemer, Nov 08 2000

Status

approved