A060357 -id:A060357 - cp's OEIS frontend

A070858 Smallest prime == 1 mod L, where L = LCM of 1 to n.

2, 3, 7, 13, 61, 61, 421, 2521, 2521, 2521, 55441, 55441, 4324321, 4324321, 4324321, 4324321, 85765681, 85765681, 232792561, 232792561, 232792561, 232792561, 10708457761, 10708457761, 26771144401, 26771144401, 401567166001, 401567166001, 18632716502401, 18632716502401

Offset: 1

Amarnath Murthy, May 16 2002

nonn

Beginning with 3, smallest prime p = a(n) such that p + k is divisible by k + 1 for each k = 1, 2, ..., n. For example: 61 --> 62, 63, 64, 65 and 66 are divisible respectively by 2, 3, 4, 5 and 6. - Robin Garcia, Jul 23 2012

Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..200 from R. J. Mathar)

Cf. A060357, A075059, A003418, A070844 to A070856, A035091.

A070858 := proc(n)
    local l,p;
    l := ilcm(seq(i,i=1..n)) ;
    for p from 1 by l do
        if isprime(p) then
            return p;
        end if;
    end do:
end proc; # R. J. Mathar, Jun 25 2013

a[n_] := Module[{m = 1, lcm = LCM @@ Range[n]}, While[!PrimeQ[m], m += lcm]; m]; Array[a, 30] (* Amiram Eldar, Mar 15 2025 *)

a(n)=my(L=lcm(vector(n,i,i)),k=1);while(!ispseudoprime(k+=L),); k \\ Charles R Greathouse IV, Jun 25 2013

More terms from Sascha Kurz, Feb 02 2003

A060358 a(n) = largest prime < lcm(1..n).

Original entry on oeis.org

5, 11, 59, 59, 419, 839, 2503, 2503, 27701, 27701, 360337, 360337, 360337, 720703, 12252197, 12252197, 232792559, 232792559, 232792559, 232792559, 5354228879, 5354228879, 26771144371, 26771144371, 80313433159, 80313433159, 2329089562799, 2329089562799

Offset: 3

N. J. A. Sloane, Apr 01 2001

nonn

Chai Wah Wu, Table of n, a(n) for n = 3..2308

Cf. A003418, A060357.

b:= proc(n) option remember; `if`(n=0, 1, ilcm(n, b(n-1))) end:
a:= n-> prevprime(b(n)):
seq(a(n), n=3..30);  # Alois P. Heinz, Feb 17 2024

Table[NextPrime[LCM@@Range[n],-1],{n,3,30}] (* Harvey P. Dale, May 28 2014 *)

a(n) = precprime(lcm([1..n])); \\ Michel Marcus, Mar 18 2018

from sympy import prevprime, lcm
def A060358(n):
    return prevprime(lcm(range(1,n+1))) # Chai Wah Wu, Jan 22 2020

A060359 a(n) = (smallest prime > k) - (largest prime < k), where k = lcm(1..n).

Original entry on oeis.org

2, 2, 2, 2, 2, 14, 18, 18, 32, 32, 54, 54, 54, 40, 62, 62, 2, 2, 2, 2, 42, 42, 30, 30, 72, 72, 44, 44, 44, 42, 42, 42, 42, 42, 96, 96, 96, 96, 126, 126, 142, 142, 142, 142, 2, 2, 142, 142, 142, 142, 122, 122, 122, 122, 122, 122, 262, 262, 98, 98

Offset: 3

N. J. A. Sloane, Apr 01 2001

nonn

Alois P. Heinz, Table of n, a(n) for n = 3..1020

Cf. A003418, A013633, A060357, A060358.

a:= n-> (m->nextprime(m)-prevprime(m))(ilcm($1..n)):
seq (a(n), n=3..100);

f[n_]:=Module[{lcmn=LCM@@Range[n]}, NextPrime[lcmn]-NextPrime[lcmn,-1]]; f/@Range[3,70]  (* Harvey P. Dale, Feb 04 2011 *)

a(n) = my(lc = lcm([1..n])); nextprime(lc+1) - precprime(lc-1); \\ Michel Marcus, Mar 20 2018

a(n) = A013633(A003418(n)). - Michel Marcus, Mar 20 2018

A060362 a(n) = Min { { smallest prime > k } - k, k - { largest prime < k } }, where k = lcm(1..n) = A003418(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 13, 13, 23, 23, 23, 17, 19, 19, 1, 1, 1, 1, 1, 1, 1, 1, 31, 31, 1, 1, 1, 1, 1, 1, 1, 1, 43, 43, 43, 43, 47, 47, 59, 59, 59, 59, 1, 1, 59, 59, 59, 59, 61, 61, 61, 61, 61, 61, 113, 113, 1, 1, 1, 97, 97, 97, 73, 73, 73, 73, 73, 73, 97

Offset: 3

N. J. A. Sloane, Apr 01 2001

nonn

Cf. A003418, A060357, A060358, A060359, A060360, A060361.

[seq( min( nextprime(A003418(n))-A003418(n), A003418(n)-prevprime(A003418(n)) ), n=3..100)];

Min[NextPrime[#]-#,#-NextPrime[#,-1]]&/@Table[LCM@@Range[n],{n,80}] (* Harvey P. Dale, Jan 01 2019 *)

a(n) = my(lcn = lcm([1..n])); min(nextprime(lcn+1)-lcn, lcn-precprime(lcn-1)); \\ Michel Marcus, Mar 29 2018

Definition corrected by Jon E. Schoenfield, Mar 18 2018

cp's OEIS Frontend

A070858 Smallest prime == 1 mod L, where L = LCM of 1 to n.

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A060358 a(n) = largest prime < lcm(1..n).

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A060359 a(n) = (smallest prime > k) - (largest prime < k), where k = lcm(1..n).

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A060362 a(n) = Min { { smallest prime > k } - k, k - { largest prime < k } }, where k = lcm(1..n) = A003418(n).

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