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.
6 is in the sequence because the 6th prime, 13, is congruent to 1 (mod 6).
import Data.List (elemIndices) a023143 n = a023143_list !! (n-1) a023143_list = 1 : map (+ 1) (elemIndices 1 a004648_list) -- Reinhard Zumkeller, Jul 30 2012, Jun 08 2011
[n: n in [1..10000] | IsIntegral((NthPrime(n)-1)/n)]; // Marius A. Burtea, Dec 30 2018
Do[ If[ IntegerQ[ (Prime[ n ] - 1) / n ], Print[ n ] ], {n, 1, 10^8} ]
n=0; print1(1); forprime(p=2,1e9, if(p%n++==1, print1(", "n))) \\ Charles R Greathouse IV, Apr 28 2015
def A023143(end): primes=[2,3] a023143_list=[1] num=3 while len(primes)<=end: num+=1 prime=False length=len(primes) for y in range(0,length): if num % primes[y]!=0: prime=True else: prime=False break if (prime): primes.append(num) for x in range(2, len(primes)): if (primes[x-1]%(x))==1: a023143_list.append(x) return a023143_list # Conner L. Delahanty, Apr 19 2014
from sympy import primerange def A023143(end): return [n+1 for n, p in enumerate(primerange(2, end)) if (p-1) % (n-1) == 0] # David Radcliffe, Jun 27 2016
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
29 is the tenth prime and 29 == -1 mod 10, so 29 is in the sequence. 31 is the eleventh prime but 31 == 9 mod 11, so 31 is not in the sequence.
divbleQ[m_, n_] := Mod[m, n] == 0; A052013 = {}; Do[p = Prime[n]; If[divbleQ[p + 1, n], AppendTo[A052013, p]], {n, 10!}]; A052013 (* Vladimir Joseph Stephan Orlovsky, Dec 08 2009 *) Select[Prime[Range[5000]], Divisible[# + 1, PrimePi[#]] &] (* Alonso del Arte, May 12 2017 *) Select[Table[{n,Prime[n]},{n,1056*10^4}],Mod[#[[2]],#[[1]]]==#[[1]]-1&][[All,2]] (* Harvey P. Dale, Oct 29 2022 *)
lista(nn) = forprime(p=2, nn, if (Mod(p,primepi(p)) + 1 == 0, print1(p, ", "))) \\ Michel Marcus, Jan 09 2015
list(lim)=my(v=List(), n, t); forprime(p=2, lim, t=(p+1)/n++; if(denominator(t)==1, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 18 2016
Mod(7,4)=3, Mod(17,7)=3.
Prime@ Select[Range[10^5], Mod[Prime[#] - 3, #] == 0 &] (* Giovanni Resta, Feb 25 2020 *)
The 10th prime is 29. Since 10 divides 29+1 = 30, 29 is in the sequence. The 12th prime is 37. Since 12 divides 37-1 = 36, 37 is in the sequence.
isA162567 := proc(p) RETURN ( (p-1) mod numtheory[pi](p) = 0 or (p+1) mod numtheory[pi](p) = 0 ) ; end: for n from 1 to 50000 do p := ithprime(n) ; if isA162567(p) then printf("%d,",p) ; fi; od: # R. J. Mathar, Jul 30 2009 with(numtheory): a := proc (n) if `mod`(ithprime(n)-1, pi(ithprime(n))) = 0 or `mod`(ithprime(n)+1, pi(ithprime(n))) = 0 then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 250000); # Emeric Deutsch, Jul 31 2009
Select[Prime[Range[11000000]],Or@@Divisible[{#-1,#+1},PrimePi[#]]&] (* Harvey P. Dale, Sep 08 2012 *)
Prime@ Select[Range[10^6], Mod[Prime[#] - 4, #] == 0 &] (* Giovanni Resta, Feb 25 2020 *)
Prime@ Select[Range[10^5], Mod[Prime[#] - 5, #] == 0 &] (* Giovanni Resta, Feb 25 2020 *)
g:= proc(t) local p; p:= ithprime(t); if p&^ t mod t = 1 then p else NULL fi end proc: map(g, [$1..1000]); # Robert Israel, Oct 31 2016
With[{no=250}, Transpose[Select[Partition[Riffle[Prime[Range[no]], Range[no]],2], PowerMod[First[#],Last[#],Last[#]]==1&]][[1]]] (* Harvey P. Dale, Jan 05 2011 *)
Prime[Select[Range[250], PowerMod[Prime[#],#,#]==1&]]
Prime@ Select[Range[10^5], Mod[Prime[#] - 7, #] == 0 &] (* Giovanni Resta, Feb 25 2020 *)
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