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A023143 Numbers n such that prime(n) == 1 (mod n). 25
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, 3140421935, 3140421892, 3140421767, 3140421744, 3140421737 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

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

MATHEMATICA

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

PROG

(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

(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

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

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

CROSSREFS

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

Sequence in context: A289206 A153485 A244048 * A085206 A238481 A058601

Adjacent sequences:  A023140 A023141 A023142 * A023144 A023145 A023146

KEYWORD

nice,nonn,easy

AUTHOR

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

EXTENSIONS

More terms from Jud McCranie, Dec 11 1999

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

STATUS

approved

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Last modified March 23 10:55 EDT 2019. Contains 321424 sequences. (Running on oeis4.)