A364706 a(n) is the least number k such that the k-th difference between consecutive practical numbers, A179651(k), equals 2*n, or -1 if no such k exists.

2, 5, 16, 33, 85, 46, 331, 188, 171, 300, 1986, 962, 3321, 968, 2316, 6514, 9974, 3219, 12162, 3831, 4588, 20585, 30099, 22005, 30465, 33485, 28874, 35901, 136396, 48483, 120127, 34145, 140589, 233364, 126080, 185421, 607164, 279989, 359002, 327768, 609867, 354143

Offset

1,1

Comments

All the practical number except for 1 are even. Therefore all the differences between consecutive practical numbers are either 1 or even.

Links

Amiram Eldar, Table of n, a(n) for n = 1..150

Formula

A179651(a(n)) = 2*n.

A005153(a(n)) = A364707(n).

Example

a(1) = 2 since A179651(2) = 2 = 2*1.
a(2) = 5 since A179651(5) = 4 = 2*2.
a(3) = 16 since A179651(16) = 6 = 2*3.

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[n_] := (ind = Position[(fct = FactorInteger[n])[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most @ fct]), _?(# > 1 &)]) == {};
seq[len_, nmax_] := Module[{s = Table[0, {len}], n = 2, prev = 2, k = 2, c = 0, i}, While[c < len && n <= nmax, n+=2; If[pracQ[n], i = (n - prev)/2; If[i <= len && s[[i]] == 0, c++; s[[i]] = k]; prev= n; k++]]; s]; seq[20, 10^6]

Crossrefs

Cf. A005153, A179651, A330870, A364707.

Sequence in context: A139022 A196025 A174988 * A053683 A305876 A082085

Adjacent sequences: A364703 A364704 A364705 * A364707 A364708 A364709

Keyword

nonn

Author

Amiram Eldar, Aug 04 2023

Status

approved