A068901 -id:A068901 - cp's OEIS frontend

A068902 Least multiple of n not less than the n-th prime.

2, 4, 6, 8, 15, 18, 21, 24, 27, 30, 33, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260

Offset: 1

Reinhard Zumkeller, Mar 05 2002

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

[n*Ceiling(NthPrime(n)/n): n in [1..60]]; // G. C. Greubel, Jun 09 2019

seq(n*ceil(ithprime(n)/n),n=1..60); # Robert Israel, Feb 27 2017

Table[n Ceiling[Prime@ n/n], {n, 60}] (* Michael De Vlieger, Feb 27 2017 *)

vector(60, n, n*ceil(prime(n)/n) ) \\ G. C. Greubel, Jun 09 2019

[n*ceil(nth_prime(n)/n) for n in (1..60)] # G. C. Greubel, Jun 09 2019

a(n) = A000040(n) + A068901(n).

a(n) = n*ceiling(prime(n)/n). - Vladeta Jovovic, Apr 06 2003

A090973 a(n) = ceiling(prime(n)/n).

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Amarnath Murthy, Jan 04 2004

			a(12) = 4 as pi(48) = 15 > 12 > pi(36) = 11.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A038605, A038606.

Cf. A068901. - Reinhard Zumkeller, Aug 16 2009

[Ceiling(NthPrime(n)/n): n in [1..120]]; // G. C. Greubel, Feb 02 2019

Table[Ceiling[Prime[n]/n], {n, 1, 120}] (* G. C. Greubel, Feb 02 2019 *)

vector(120, n, ceil(prime(n)/n)) \\ G. C. Greubel, Feb 02 2019

[ceil(nth_prime(n)/n) for n in (1..120)] # G. C. Greubel, Feb 02 2019

For n > 1, a(n) = A038605(n)+1. - David Wasserman, Feb 23 2006

a(A038606(n)) = n+1. - Reinhard Zumkeller, Aug 16 2009

More terms from David Wasserman, Feb 23 2006

A131848 Least nonnegative number which when added to the n-th semiprime gives a multiple of n.

Original entry on oeis.org

0, 0, 0, 2, 1, 3, 0, 2, 2, 4, 0, 2, 4, 4, 6, 2, 2, 3, 2, 3, 5, 4, 4, 3, 1, 1, 26, 27, 1, 3, 2, 3, 5, 7, 34, 33, 33, 34, 37, 39, 1, 3, 0, 43, 1, 43, 46, 1, 2, 4, 49, 50, 0, 1, 54, 55, 51, 54, 53, 55, 57, 54, 51, 54, 57, 59, 62, 63, 63, 66, 69, 71, 1, 3, 4, 2, 73, 75, 69, 71

Offset: 1

Jonathan Vos Post, Oct 04 2007

This is to semiprimes A001358 as A068901 is to primes A000040.

			a(1) = 0 because 1 | (0+semiprime(1)=4).
a(6) = 3 because 6 | (3+semiprime(3)=3+15=18).
a(25) = 1 because 25 | (1+semiprime(25)=1+74=75).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A001358, A068901.

lnn[{s_,n_}]:=If[Divisible[s,n],0,n-Mod[s,n]]; lnn/@Module[{sp=Select[ Range[ 300], PrimeOmega[#] ==2&], len},len=Length[sp];Thread[{sp,Range[len]}]] (* Harvey P. Dale, Mar 23 2013 *)

a(n) = MIN{k=>0 such that n|(k+A001358(n))}.

More terms from R. J. Mathar, Jan 15 2008

A364633 a(n) is the smallest nonnegative number k such that prime(n) + k is divisible by n + 1.

Original entry on oeis.org

0, 0, 3, 3, 1, 1, 7, 8, 7, 4, 5, 2, 1, 2, 1, 15, 13, 15, 13, 13, 15, 13, 13, 11, 7, 7, 9, 9, 11, 11, 1, 1, 33, 1, 31, 34, 33, 32, 33, 32, 31, 34, 29, 32, 33, 36, 29, 22, 23, 26, 27, 26, 29, 24, 23, 22, 21, 24, 23, 24, 27, 22, 13, 14, 17, 18, 9, 8, 3, 6, 7, 6, 3, 2, 1, 2, 1

Offset: 1

Andres Cicuttin, Jul 30 2023

The sequence presents a pattern with large discontinuities at regular intervals in the logarithmic plot (See plots in Links).

			The following table shows the first 10 terms where the fourth column, a(n), plus the third column, prime(n), is divisible by the second column n+1:
   n   n+1 prime(n) a(n)
   1    2     2       0
   2    3     3       0
   3    4     5       3
   4    5     7       3
   5    6    11       1
   6    7    13       1
   7    8    17       7
   8    9    19       8
   9   10    23       7
  10   11    29       4

Andres Cicuttin, Log-log plot
Andres Cicuttin, Linear plot

Cf. A068901.

a[n_]:=Module[{k},k=0;
While[Mod[Prime[n]+k,n+1]!=0,k++];k];
Table[a[n],{n,1,70}]

a(n) = my(k=0, p=prime(n)); while ((p+k) % (n+1), k++); k; \\ Michel Marcus, Sep 05 2023

from sympy import prime
def A364633(n): return (n+1)*(prime(n)//(n+1)+1)-prime(n) if n>2 else 0 # Chai Wah Wu, Sep 04 2023

a(n) = Min_{k | (n+1) divides (prime(n)+k)}.

a(n) = (n+1)*ceiling(prime(n)/(n+1)) - prime(n)

A379014 Least number k such that prime(n) + prime(k) is a multiple of n, or -1 if no such number exists.

Original entry on oeis.org

1, 2, 4, 3, 8, 3, 5, 3, 6, 5, 1, 5, 5, 6, 6, 5, 14, 5, 15, 10, 5, 11, 26, 4, 2, 2, 3, 3, 4, 4, 17, 10, 18, 11, 18, 10, 34, 27, 19, 19, 19, 10, 19, 20, 21, 11, 20, 7, 19, 20, 21, 21, 111, 8, 21, 7, 21, 8, 65, 8, 23, 7, 20, 21, 68, 6, 20, 2, 19, 20, 1, 21, 20, 20

Offset: 1

Jean-Marc Rebert, Dec 13 2024

nonn

Indices n where a(n)=1 correspond with terms of A092044. - Bill McEachen, Dec 21 2024

Cf. A000040, A000720, A068901, A294639.

a[n_]:=Module[{k=1},While[!Divisible[Prime[n]+Prime[k],n], k++]; k]; Array[a,74] (* Stefano Spezia, Dec 13 2024 *)

a(n) = my(k=1, p=prime(n)); while ((p+prime(k)) % n, k++); k; \\ Michel Marcus, Dec 13 2024

a(n) = A000720(A294639(n)). - Pontus von Brömssen, Dec 13 2024

cp's OEIS Frontend

A068902 Least multiple of n not less than the n-th prime.

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A090973 a(n) = ceiling(prime(n)/n).

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A131848 Least nonnegative number which when added to the n-th semiprime gives a multiple of n.

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A364633 a(n) is the smallest nonnegative number k such that prime(n) + k is divisible by n + 1.

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A379014 Least number k such that prime(n) + prime(k) is a multiple of n, or -1 if no such number exists.

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Mathematica

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