This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a004648 n = a004648_list !! (n-1) a004648_list = zipWith mod a000040_list [1..] -- Reinhard Zumkeller, Jul 30 2012
[(NthPrime(n) mod n): n in [1..100]]; // Vincenzo Librandi, Apr 06 2011
A004648 := proc(n) modp(ithprime(n),n) ; end proc: # R. J. Mathar, Dec 02 2014
Table[Mod[Prime[n], n], {n, 100}] (* Zak Seidov, Apr 25 2005 *)
for(n=1,100,print1(prime(n)%n,","))
from sympy import prime; print([prime(i) % i for i in range(1, 101)]) # Jwalin Bhatt, Jul 29 2025
def A004648(n): return (nth_prime(n)%n) [A004648(n) for n in range(1,101)] # G. C. Greubel, Apr 20 2023
10 is a member because the 10th prime, 29, is congruent to -1 mod 10.
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[Mod[p = NextPrim[p], n] == n - 1, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
isok(n) = Mod(prime(n), n) == -1; \\ Michel Marcus, Jul 24 2018
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 2, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 10, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
n=0; forprime(p=2,1e9, if(Mod(p,n++)==10, print1(n", "))) \\ Charles R Greathouse IV, Apr 29 2015
def A023152(max) : terms = [] p = 2 for n in range(1,max+1) : if (p - 10) % n == 0 : terms.append(n) p = next_prime(p) return terms # Eric M. Schmidt, Feb 05 2013
p = 1; Do[ If[ Mod[p = NextPrime[p], n] == 8, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
def A023150(max): terms = [] p = 2 for n in range(1, max+1) : if (p - 8) % n == 0 : terms.append(n) p = next_prime(p) return terms # Eric M. Schmidt, Feb 05 2013
204475053103 = prime(8179002124) and 204475053103 = 25*8179002124 + 3.
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 3, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
Select[Range[100000], Mod[Prime[#] - 3, #] == 0 &] (* T. D. Noe, Feb 05 2013 *)
def A023145(max) : terms = [] p = 2 for n in range(1, max+1) : if (p - 3) % n == 0 : terms.append(n) p = next_prime(p) return terms # Eric M. Schmidt, Feb 05 2013
The 75th prime is 379 and 379 == 4 (mod 75). Hence 75 is in the sequence. The 76th prime is 383, but 383 == 3, not 4, (mod 76). So 76 is not in the sequence.
nextPrime[n_] := Block[{k = n + 1}, While[!PrimeQ[k], k++]; k]; p = 1; Do[If[Mod[p = nextPrime[p], n] == 4, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
Select[Range[1000], Mod[Prime[#], #] == 4 &] (* Alonso del Arte, Nov 16 2018 *)
def A023146(max) : terms = [] p = 2 for n in range(1, max+1) : if (p - 4) % n == 0 : terms.append(n) p = next_prime(p) return terms # Eric M. Schmidt, Feb 05 2013
p = 1; Do[ If[ Mod[p = NextPrime[p], n] == 5, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
p = 1; Do[ If[ Mod[p = NextPrime[p], n] == 7, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
def A023149(max) : terms = [] p = 2 for n in range(1, max+1) : if (p - 7) % n == 0 : terms.append(n) p = next_prime(p) return terms # Eric M. Schmidt, Feb 05 2013
Comments