A174817 - OEIS

%I #31 Oct 12 2024 21:31:23

%S 808017424794512875886459904961710757005754367999999957,

%T 808017424794512875886459904961710757005754367999999947,

%U 808017424794512875886459904961710757005754368000000083,808017424794512875886459904961710757005754367999999803,808017424794512875886459904961710757005754368000000283

%N Near primes to Mnr = A001228(26) = 808017424794512875886459904961710757005754368000000000, also called the Monster number, cf. A003131.

%C Sorted by increasing distance to Mnr = abs(A174818(n)).

%H Reinhard Zumkeller, <a href="/A174817/b174817.txt">Table of n, a(n) for n = 1..146</a>

%H Dario A. Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MonsterGroup.html">Sporadic Group</a>

%F a(n) = Mnr + A174818(n).

%e a(1) = Mnr - 43 = 808017424794512875886459904961710757005754367999999957 is the nearest prime to Mnr;

%e a(3) = Mnr + 83 = 808017424794512875886459904961710757005754368000000083 is the smallest prime greater than Mnr; remarkably, (a(143),a(141)) = (Mnr-9511,Mnr-9509) is a twin prime pair.

%t With[{mnr=808017424794512875886459904961710757005754368000000000},SortBy[ {#,Abs[ #-mnr]}&/@Table[NextPrime[mnr,n],{n,{-4,-3,-2,-1,1,2,3,4}}],Last]][[All,1]] (* _Harvey P. Dale_, Nov 14 2021 *)

%Y Cf. A001228, A003131, A174818.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 02 2010

%E a(5) aligned with b-file by _Georg Fischer_, Jul 11 2022