A305729 Numbers k such that A000010(k) = A023900(k) and A000010(A023900(k)) = A023900(A000010(k)).

1, 14, 22, 46, 94, 118, 166, 214, 334, 358, 422, 454, 526, 662, 694, 718, 766, 926, 934, 958, 1006, 1094, 1126, 1142, 1174, 1382, 1438, 1678, 1718, 1726, 1774, 1822, 1934, 1966, 2038

Offset

1,2

Comments

For known terms with n > 1:

- a(n) and phi(a(n)) are squarefree integers with an even number of prime factors. For example a(5) = 94 = 2 * 47, and phi(a(5)) = 46 = 2 * 23.

- When omega(a(n)) = omega(phi(a(n)) = 2 then a(n)/2 are the Safe primes (see A005385).

- When omega(a(n)) = omega(phi(a(n)) = 2 then ((a(n)/2)-1)/2 = phi(a(n))/2 are the Sophie Germain primes (see A005384).

Links

Table of n, a(n) for n=1..35.

Example

1 is a term because A000010(1) = A023900(2) and A000010(A023900(1)) = A023900(A000010(1)).

Crossrefs

Cf. A000010, A023900, A005384, A005385.

Cf. Subsequence of A244466.

Cf. Subsequence of A306146.

Sequence in context: A043114 A043894 A054276 * A344135 A167332 A291160

Adjacent sequences: A305726 A305727 A305728 * A305730 A305731 A305732

Keyword

nonn

Author

Torlach Rush, Aug 11 2018

Status

approved