A068902 -id:A068902 - cp's OEIS frontend

A283053 Numbers k such that A068902(k+1) <= A068902(k).

69, 181, 1052, 6457, 6460, 6466, 40083, 100362, 251707, 251722, 251736, 251741, 637236, 637322, 637326, 637333, 4124458, 4124467, 4124587, 10553439, 10553444, 10553454, 10553478, 10553502, 10553505, 10553547, 10553568, 10553573, 10553575, 10553818, 10553827

Offset: 1

Robert Israel, Feb 27 2017

nonn

Numbers k for which k*floor(ceiling(prime(k+1)/(k+1))*(1+1/k)) < prime(k).

			For n=1, A068902(69) = 414 <= A068902(70) = 350.

Cf. A068902.

P = primes(10^8);
N = numel(P);
R = [1:N] .* ceil(P ./ [1:N]);
Rd = R(2:end) - R(1:end-1);
find(Rd <= 0)

Flatten@ Position[Differences@ Table[n Ceiling[Prime@ n/n], {n, 10^7}], k_ /; k <= 0] (* Michael De Vlieger, Feb 27 2017 *)

More terms from Michael De Vlieger, Feb 27 2017

A068901 Least number that when added to the n-th prime gives a multiple of n.

Original entry on oeis.org

0, 1, 1, 1, 4, 5, 4, 5, 4, 1, 2, 11, 11, 13, 13, 11, 9, 11, 9, 9, 11, 9, 9, 7, 3, 3, 5, 5, 7, 7, 28, 29, 28, 31, 26, 29, 28, 27, 28, 27, 26, 29, 24, 27, 28, 31, 24, 17, 18, 21, 22, 21, 24, 19, 18, 17, 16, 19, 18, 19, 22, 17, 8, 9, 12, 13, 4, 3, 67, 1

Offset: 1

Reinhard Zumkeller, Mar 05 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A090973. - Reinhard Zumkeller, Aug 16 2009

Cf. A000040, A068902.

a068901 n = head $
   filter ((== 0) . (`mod` fromIntegral n) . (+ a000040 n)) $ [0..]
-- Reinhard Zumkeller, Feb 18 2012

f[n_] := Module[{p=Prime[n]}, n*Ceiling[p/n]-p]; Array[f,100]  (* Harvey P. Dale, Apr 06 2011 *)

a(n) = Min_{k | n divides (prime(n)+k)}.
a(n) = A068902(n) - A000040(n).
a(n) = n*ceiling(prime(n)/n) - prime(n). - Vladeta Jovovic, Apr 06 2003

A156902 Primes p such that there is no multiple of (the order of p among the primes) between p and q, where q is the smallest prime > p.

Original entry on oeis.org

11, 13, 17, 19, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 101, 103, 107, 109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313

Offset: 1

Leroy Quet, Feb 17 2009

nonn

If pi(p) is the order of the prime p, then p is included in the sequence if pi(p)*ceiling(p/pi(p)) > the (pi(p)+1)th prime.

The sequence of primes not in the list is less dense: 2, 3, 5, 7, 23, 29, 31, 89, 97, 113, 317, 331, 337, 349, 353, 359, 997, 1069, 1091, 1109, 1117, 1123, 1129, 3049, 3061, 3067, 3079, 3083, 3089, ... - R. J. Mathar, Feb 21 2009

			37 is the 12th prime. 41 is the 13th prime. Since there is no multiple of 12 between 37 and 41, then 37 is included in the sequence.

Cf. A068902.

for n from 1 to 300 do p := ithprime(n) ; q := nextprime(p) ; if n*floor(q/n) < p then printf("%d,",p) ; fi; od: # R. J. Mathar, Feb 21 2009

Extended by R. J. Mathar, Feb 21 2009

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A283053 Numbers k such that A068902(k+1) <= A068902(k).

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A068901 Least number that when added to the n-th prime gives a multiple of n.

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A156902 Primes p such that there is no multiple of (the order of p among the primes) between p and q, where q is the smallest prime > p.

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