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<a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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a(1) = 1, a(n) = A000040(A001222(n)) * A064989(n) = A105560(n) * A064989(n).

Cf. A000041, A243051, A243072, A243073, A226062, A242422, A242423, A122111, A105560, A000040, A001222, A064989, A056239.

Integer sequence induced by Bulgarian solitaire operation on partition list A112798: a(1) = 1, a(n) = A000040(A001222(n)) * A064989(n).

In "Bulgarian solitaire" a deck of cards or another finite set of objects is divided into one or more piles, and the "Bulgarian operation" is performed by taking one card from each pile, and making a new pile of them, which is added to the remaining set of piles remaining. Essentially, this operation is a function whose domain and range are unordered integer partitions (cf. A000041) and which preserves the total size of a partition (the sum of its parts). This sequence is induced when the operation is implemented on the partitions as ordered by the list A112798.

a(A000079(n)) = A000040(n) for all n>=1.

In "Bulgarian solitaire" a deck of cards or another finite set of objects is divided into one or more piles, and the "Bulgarian operation" is performed by taking one card from each pile, and making a new pile of them, which is added to the set of piles remaining. Essentially, this operation is a function whose domain and range are nonordered unordered integer partitions (cf. A000041) and which preserves the total size of a partition (the sum of its parts). This sequence is induced when the operation is implemented on the partitions as ordered by the list A112798.

Cf. A000041, A243051, A243072, A243073, A226062, A242422, A242423, A122111, A000040, A001222, A064989, A056239.

In "Bulgarian solitaire" a deck of cards or another finite set of objects is divided into one or more piles, and the "Bulgarian operation" is performed by taking one card from each pile, and making a new pile of them, which is added to the set of piles remaining. Essentially, this operation is a function whose domain and range are nonordered integer partitions (cf. A000041) and which preserves the total size of a partition (the sum of its parts). This sequence is induced when the operation is implemented on the partitions as ordered by the list A112798, from which follows that we, for example, have: A056239(a(n)) = A056239(n) for all n.

a(A000079(n)) = A000040(n) for all n>=1. [Maps powers of two to primes.]

A056239(a(n)) = A056239(n) for all n.

Cf. A000041, A243051, A226062, A242422, A242423, A122111, A000040, A001222, A064989, A056239.

In "Bulgarian solitaire" a deck of cards or another finite set of objects is divided into one or more piles, and the "Bulgarian operation" is performed by taking one card from each pile, and making a new pile of them, which is added to the set of piles remaining. Essentially, this operation is a function whose domain and range are nonordered integer partitions (cf. A000041) and which preserves the total size of a partition (the sum of its parts). This sequence is induced when the operation is implemented on the partitions as ordered by the list A112798, from which follows that we, for example, have: A056239(a(n)) = A056239(n) for all n.

In "Bulgarian solitaire" a deck of cards or another finite set of objects is divided into one or more piles, and the "Bulgarian operation" is performed by taking one card from each pile, and making a new pile of them. The question originally posed was: on what condition the resulting partitions will eventually reach a fixed point, that is, a collection of piles that will be unchanged by the operation. See Martin Gardner reference and the Wikipedia-page.

Because Bulgarian solitaire operation doesn't change the total sum we have: A056239(a(n)) = A056239(n) for all n.

Maps powers of two to primes: a(A000079(n)) = A000040(n) for all n>=1.

a(A000079(n)) = A000040(n) for all n>=1. [Maps powers of two to primes.]

Row 1 of A243070 (table which gives successive "recursive iterates" of this sequence) and converges towards A122111).