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 A189409 a(n) = prime(n)#^2 + 1, where prime(n)# is the n-th primorial (A002110). 3
 2, 5, 37, 901, 44101, 5336101, 901800901, 260620460101, 94083986096101, 49770428644836901, 41856930490307832901, 40224510201185827416901, 55067354465423397733736101, 92568222856376731590410384101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A variation of Euclid numbers. It is unknown whether or not numbers in this sequence are always squarefree. It is unknown whether or not there exist infinitely many primes in this sequence. For Euclid numbers see A006862. Comment from Abhiram R Devesh, Jan 23 2013: (Start) (i) The last 3 digits of an entry is always either 101 or 901 (with the exception of the first 3 terms), (ii) the thousand's place digit is an even number. (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..190 E.W. Weisstein, Integer Sequence Primes Eric W. Weisstein's World of Mathematics, Euclid's Theorem FORMULA a(n)=(E(n)-1)^2+1, where E(n) is the n-th Euclid number. EXAMPLE (p_16#)^2+1 = 1062053250251407755176413469419400772901 is prime. MATHEMATICA Table[Product[Prime[n]^2, {n, 1, k}] + 1, {k, 0, 16}] Join[{2}, FoldList[Times, Prime[Range]]^2+1] (* Harvey P. Dale, Jan 15 2019 *) PROG (Python) from functools import reduce import numpy as np def factors(n):     return reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)) mul = 1 for i in range(1, 20):     if len(factors(i))<3:         mul *= i*i         print(mul+1, factors(mul+1)) # Abhiram R Devesh, Jan 23 2013 (PARI) list(maxx)={n=prime(1); cnt=0; print("0  2"); while(n<=maxx, q=(prodeuler(p=1, n, p))^2+1; cnt++; print(cnt, "  ", q); n=nextprime(n+1)); } \\ Bill McEachen, Feb 03 2014 CROSSREFS A002110, A006862, A014545, A210482 (subsequence of primes). Sequence in context: A107633 A041959 A051739 * A222318 A084436 A210482 Adjacent sequences:  A189406 A189407 A189408 * A189410 A189411 A189412 KEYWORD nonn,easy AUTHOR John M. Campbell, Apr 21 2011 EXTENSIONS Typo in Mma fixed by Vincenzo Librandi, Feb 04 2014 STATUS approved

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Last modified September 18 07:30 EDT 2021. Contains 347510 sequences. (Running on oeis4.)