A049536 -id:A049536 - cp's OEIS frontend

A053609 Primes of form x^2+1 where x = LCM(1,2,...,k) for some k.

2, 5, 37, 176401, 129859329601, 516625648014869290354797521879383114125823989794742396526049715541246671360001

Offset: 1

Labos Elemer, Feb 09 2000

The next term has k > 10^4, if it exists. - Amiram Eldar, Aug 23 2024

Cf. A049536, A046029, A051739, A051418, A051451, A053608.

Select[FoldList[LCM, 1, Select[Range[100], PrimePowerQ]]^2 + 1, PrimeQ] (* Amiram Eldar, Aug 23 2024 *)

a(n) = A053608(A053608(n)) = A053608(n)^2 + 1. - Amiram Eldar, Aug 23 2024

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

Original entry on oeis.org

5, 11, 59, 419, 232792559, 442720643463713815199

Offset: 1

Labos Elemer, Nov 08 2000

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

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

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

Cf. A003418, A051451, A057706.

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

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

cp's OEIS Frontend

A053609 Primes of form x^2+1 where x = LCM(1,2,...,k) for some k.

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