A023143 Numbers k such that prime(k) == 1 (mod k).

1, 2, 5, 6, 12, 14, 181, 6459, 6460, 6466, 100362, 251712, 251732, 637236, 10553504, 10553505, 10553547, 10553827, 10553851, 10553852, 69709709, 69709724, 69709728, 69709869, 69709961, 69709962, 179992920, 179992922, 179993170, 465769815, 465769819, 465769840, 3140421737, 3140421744, 3140421767, 3140421892, 3140421935

Offset: 1

Author

David W. Wilson and G. L. Honaker, Jr., Jun 14 1998

Keywords

• nonn
• nice

Comments

A004648(a(n)) <= 1. - Reinhard Zumkeller, Jul 30 2012

Examples

			6 is in the sequence because the 6th prime, 13, is congruent to 1 (mod 6).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..94

Crossrefs

Cf. A048891, A045924, A052013, A023144, A023145, A023146, A023147, A023148, A023149, A023150, A023151, A023152.

Programs

Haskell

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

Magma

[n: n in [1..10000] | IsIntegral((NthPrime(n)-1)/n)]; // Marius A. Burtea, Dec 30 2018

Mathematica

Do[ If[ IntegerQ[ (Prime[ n ] - 1) / n ], Print[ n ] ], {n, 1, 10^8} ]

PARI

n=0; print1(1); forprime(p=2,1e9, if(p%n++==1, print1(", "n))) \\ Charles R Greathouse IV, Apr 28 2015

Python

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

Python

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

Extensions

More terms from Jud McCranie, Dec 11 1999

a(30)-a(37) from Zak Seidov, Apr 19 2014

Terms a(33)-a(37) sorted in correct order by Giovanni Resta, Feb 23 2020