A171434 -id:A171434 - cp's OEIS frontend

A023149 Numbers k such that prime(k) == 7 (mod k).

1, 2, 4, 6, 18, 36, 78, 191, 6456, 6457, 40080, 40081, 637324, 637326, 637344, 10553425, 10553434, 10553477, 10553502, 10553573, 10553854, 27066988, 27067126, 69709680, 69709736, 69709940, 465769818, 3140421716, 3140421740, 3140421743

Offset: 1

David W. Wilson

nonn

Giovanni Resta, Table of n, a(n) for n = 1..71

Cf. A171434, A092049, A023143, A023144, A023145, A023146, A023147, A023148, A023150, A023151, A023152.

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

More terms from Robert G. Wilson v, Feb 18 2004
a(27)-a(31) from Robert G. Wilson v, Feb 22 2006
First four terms inserted by Eric M. Schmidt, Feb 05 2013

A360789 Least prime p such that p mod primepi(p) = n.

Original entry on oeis.org

2, 3, 5, 7, 379, 23, 401, 61, 59, 29, 67, 71, 467, 79, 83, 179, 431, 89, 176557, 191, 24419, 491, 97, 101, 499, 1213, 3169, 3191, 523, 229, 3187, 223, 3203, 8609, 3163, 251, 176509, 257, 24509, 263, 3253, 269, 547, 3347, 1304867, 293

Offset: 0

Robert G. Wilson v, Feb 20 2023

nonn

Inspired by A048891.

			For n=0, prime p=2 has p mod primepi(p) = 2 mod 1 = 0 so that a(0) = 2.
For n=4, no prime has p mod primepi(p) = 4 until reaching p=379 which is 379 mod 75 = 4, so that a(4) = 379.

Robert G. Wilson v, Table of n, a(n) for n = 0..19217

Cf. A038625, A004648, A048891, A052013, A073325, A073436, A162567, A171430, A171431, A171432, A171434.

V:= Array(0..100): count:= 0:
p:= 1:
for k from 1 while count < 101 do
  p:= nextprime(p);
  v:= p mod k;
  if v <= 100 and V[v] = 0 then V[v]:= p; count:= count+1 fi;
od:
convert(V,list); # Robert Israel, Feb 28 2023

t[_] := 0; p = 2; pi = 1; While[p < 1400000, m = Mod[p, pi]; If[m < 100 && t[m] == 0, t[m] = p]; p = NextPrime@p; pi++]; t /@ Range[0, 99]

a(n)={my(k=n); forprime(p=prime(n+1), oo, k++; if(p%k ==n, return(p)))} \\ Andrew Howroyd, Feb 21 2023

from sympy import prime, nextprime
def A360789(n):
    p, m = prime(n+1), n+1
    while p%m != n:
        p = nextprime(p)
        m += 1
    return p # Chai Wah Wu, Mar 18 2023

a(n) = prime(A073325(n+1)). - Kevin Ryde, Feb 21 2023

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A023149 Numbers k such that prime(k) == 7 (mod k).

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A360789 Least prime p such that p mod primepi(p) = n.

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