A060234 a(n) = (prime(n) mod (prime(n+1)-prime(n))).

0, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 1, 3, 5, 5, 1, 1, 3, 1, 1, 3, 5, 1, 1, 1, 3, 1, 1, 1, 3, 5, 1, 9, 1, 1, 1, 3, 5, 5, 1, 1, 1, 1, 1, 7, 7, 3, 1, 1, 5, 1, 1, 5, 5, 5, 1, 1, 1, 1, 3, 13, 3, 1, 1, 9, 1, 7, 1, 1, 5, 7, 1, 1, 3, 5, 5, 1, 1, 9, 1, 1, 1, 1, 3, 5, 1, 1, 1, 3, 11, 7, 3, 3, 3, 5, 5, 1, 1, 1, 7, 5, 5

Offset

1,4

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

Formula

a(n) = prime(n) mod (prime(n+1) - prime(n)) where prime(n) is the n-th prime.

Example

7 is followed by 11. 7 mod (11-7) = 7 mod 4 = 3. So a(4) = 3.
This residue is always odd: 3 = 1*2 + 1, 7 = 1*4 + 3, 23 = 3*6 + 5, etc.

Maple

seq(ithprime(i) mod (ithprime(i+1)-ithprime(i)), i=1..2000); # Muniru A Asiru, Jan 29 2018

Mathematica

Table[Mod[Prime[n], Prime[n+1] - Prime[n]], {n, 1, 100}] (* Vincenzo Librandi, Jan 29 2018 *)

Prog

(PARI) a(n) = prime(n) % (prime(n+1) - prime(n)); \\ Michel Marcus, Nov 26 2013
(GAP) P:=Filtered([1..10^7], IsPrime);;
P1:=List([1..Length(P)-1], n -> P[n+1] - P[n]);;
A060234 := List([1..Length(P1)], n->P[n] mod P1[n]); # Muniru A Asiru, Jan 29 2018
(Magma) [NthPrime(n) mod (NthPrime(n+1)-NthPrime(n)): n in [1..100]]; // Vincenzo Librandi, Jan 29 2018
(SageMath)
def A060234(n): return nth_prime(n)%(nth_prime(n+1) - nth_prime(n))
[A060234(n) for n in range(1, 121)] # G. C. Greubel, Nov 03 2024

Crossrefs

Cf. A000040, A001223.

Sequence in context: A076476 A243200 A016733 * A131270 A109223 A263009

Adjacent sequences: A060231 A060232 A060233 * A060235 A060236 A060237

Keyword

nonn

Author

Labos Elemer, Mar 21 2001

Status

approved