A243068 Fixed points of A242420.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31, 32, 36, 37, 41, 43, 47, 48, 49, 53, 54, 59, 61, 63, 64, 65, 67, 70, 71, 72, 73, 79, 81, 83, 89, 96, 97, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 133, 137, 139, 144

Offset

1,2

Comments

A number n is present if its prime factorization n = p_a * p_b * p_c * ... * p_i * p_j * p_k^e_k, where a <= b <= c <= ... <= i <= j < k are the indices of prime factors, not necessarily all distinct, except that j < k, and the greatest prime divisor p_k [with k = A061395(n)] may occur multiple times, satisfies the condition that the first differences of those prime indices (a-0, b-a, c-b, ..., j-i, k-j) form a palindrome.

Links

Antti Karttunen, Table of n, a(n) for n = 1..2185

Example

4 = p_1^2 is present, as the first differences (deltas) of the prime indices (excluding the extra copies of the largest prime factor 2), form a palindrome: (1-0) = (1).
18 = 2*3*3 = p_1 * p_2 * p_2 is present, as the deltas of the indices of its nondistinct prime factors, (excluding the extra copies of the largest prime factor 3) form a palindrome: (1-0, 2-1) = (1,1).
60 = 2*2*3*5 = p_1 * p_1 * p_2 * p_3 is NOT present, as the deltas of prime indices (1-0, 1-1, 2-1, 3-2) = (1,0,1,1) do NOT form a palindrome.
Also, any of the cases mentioned in the Example section of A243058 as being present there, are also present in this sequence.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A243068 (FIXED-POINTS 1 1 A242420))

Crossrefs

Fixed points of A242420.

Differs from A242413 for the first time at n=36, where a(36)=61, while A242413(36)=60.

A000040 and A243058 are subsequences.

Cf. A242414, A242417.

Sequence in context: A068998 A072303 A242413 * A342339 A081061 A317589

Adjacent sequences: A243065 A243066 A243067 * A243069 A243070 A243071

Keyword

nonn

Author

Antti Karttunen, Jun 01 2014

Status

approved