A369615 Powers of primes (A000961) whose neighbors have a prime number as their greatest odd divisor.

4, 11, 13, 23, 25, 27, 47, 81, 193, 383, 2187, 1594323

Offset

1,1

Comments

From Jon E. Schoenfield, Jan 28 2024: (Start)

If it exists, a(13) > 10^2000.

Conjecture: a(12) = 1594323 is the final term of the sequence.

(End)

Links

Table of n, a(n) for n=1..12.

Example

(prime = greatest odd divisor of a(n)-1; a(n); prime = greatest odd divisor of a(n)+1): (3; 4; 5), (5; 11; 3), (3; 13; 7), (11; 23; 3), (3; 25; 13), (13; 27; 7), (23; 47; 3), (5; 81; 41), (3; 193; 97), (191; 383; 3), (1093; 2187; 547), (797161; 1594323; 398581).

Mathematica

q[n_] := PrimeQ[n/2^IntegerExponent[n, 2]]; Select[Range[2*10^6], PrimePowerQ[#] && And @@ q /@ {# - 1, # + 1} &] (* Amiram Eldar, Jan 28 2024 *)

Prog

(Magma) [k: k in [2..1600000] | #Divisors(2*k-2)-#Divisors(k-1) eq 2 and
 #PrimeDivisors(k) eq 1 and #Divisors(2*k+2)-#Divisors(k+1) eq 2];

Crossrefs

Intersection of A000961 and A369329.

Cf. A038550.

Comparable sequences: A275598, A343973.

Sequence in context: A228003 A347561 A234903 * A095797 A205846 A204542

Adjacent sequences: A369612 A369613 A369614 * A369616 A369617 A369618

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Jan 27 2024

Status

approved