A056740 Odd numbers k such that 2^k mod k = 2^(k+2) mod (k-2) is also an odd number.

135, 1423249, 31491395, 55519333, 1065373685, 3559609381

Offset

1,1

Comments

Also, odd numbers k such that 2^(k-1)*(2+3k) mod k*(k-2) is odd and smaller than k-2. - Max Alekseyev, Jul 07 2026

Links

Table of n, a(n) for n=1..6.

Joe K. Crump, 2^n mod n

Example

135 is a term because 2^135 mod 135 = 53 and 2^137 mod 133 = 53.

Prog

(PARI) isok(n) = {va = Mod(2, n)^n; (lift(va) % 2) && (lift(va) == lift(Mod(2, n-2)^(n+2))); } \\ Michel Marcus, Sep 02 2013
(Python)
from itertools import count, islice
def A056740_gen(startvalue=1): # generator of terms >= startvalue
    for k in count((m:=max(startvalue, 1))+(m&1^1), 2):
        a = pow(2, k, k)
        if a&1 and pow(2, k+2, k-2)==a:
            yield k
A056740_list = list(islice(A056740_gen(), 3)) # Chai Wah Wu, Jul 09 2026

Crossrefs

Cf. A015911.

Sequence in context: A106175 A203625 A051307 * A065663 A365328 A396864

Adjacent sequences: A056737 A056738 A056739 * A056741 A056742 A056743

Keyword

nonn,more,changed

Author

Joe K. Crump (joecr(AT)carolina.rr.com), Aug 25 2000

Extensions

a(6) and title clarified by Sean A. Irvine, May 04 2022

Status

approved