A339567 -id:A339567 - cp's OEIS frontend

A339566 Primes p such that A007088(p) == 1 (mod p).

5, 137, 3967, 25087, 242899421

Offset: 1

Robert Israel, Dec 09 2020

			a(3) = 3967 is in the sequence because 3967 = 111101111111_2 and 111101111111 == 1 (mod 3967).

Cf. A007088, A339544.

Primes in A339567.

p:= 1: R:= NULL:
while p < 3*10^8 do
p:= nextprime(p);
if convert(p,binary) mod p = 1 then R:= R, p fi
od:
R;

from sympy import nextprime
A339566_list, p = [], 2
while p < 10**10:
    if int(bin(p)[2:]) % p == 1:
        A339566_list.append(p)
    p = nextprime(p) # Chai Wah Wu, Dec 14 2020

A355297 a(n) = A007088(n) mod n.

Original entry on oeis.org

0, 0, 2, 0, 1, 2, 6, 0, 2, 0, 10, 8, 9, 4, 1, 0, 5, 2, 17, 0, 0, 12, 14, 8, 1, 12, 22, 12, 23, 10, 13, 0, 11, 16, 16, 20, 16, 18, 37, 0, 18, 0, 4, 32, 31, 2, 14, 32, 45, 10, 4, 16, 20, 4, 1, 8, 22, 56, 32, 40, 20, 6, 42, 0, 41, 44, 36, 24, 15, 20, 5, 56, 25, 12, 61, 28, 24, 58, 23, 0

Offset: 1

Ctibor O. Zizka, Jun 27 2022

a(n) = 0 see A032533, a(n) = 1 see A339567.

			n = 7; a(7) = A007088(7) mod 7 = 111 mod 7 = 6.

Cf. A007088, A032532, A032533, A339567.

a[n_] := Mod[FromDigits[IntegerDigits[n, 2]], n]; Array[a, 100] (* Amiram Eldar, Jun 27 2022 *)

a(n) = A007088(n) mod n. a(n) = A007088(n) - n * floor(A007088(n)/n).

cp's OEIS Frontend

A339566 Primes p such that A007088(p) == 1 (mod p).

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