A352322 Starts of runs of 3 consecutive Pell-Niven numbers (A352320).

4, 28, 110, 168, 984, 1024, 3123, 3514, 5740, 6783, 6923, 8584, 12664, 16744, 18160, 19670, 23190, 23470, 24030, 34503, 34643, 36304, 40384, 45880, 47390, 50910, 51190, 51750, 57607, 61640, 68104, 73600, 78403, 78630, 78910, 79470, 86674, 89360, 95824, 101320

Offset

1,1

Comments

Conjecture: There are no runs of 4 consecutive Pell-Niven numbers (checked up to 2*10^8).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4 is a term since 4, 5 and 6 are all Pell-Niven numbers: the minimal Pell representation of 4, A317204(20) = 20, has the sum of digits 2+0 = 2 and 4 is divisible by 2, the minimal Pell representation of 5, A317204(5) = 100, has the sum of digits 1+0+0 = 1 and 5 is divisible by 1, and the minimal Pell representation of 6, A317204(6) = 101, has the sum of digits 1+0+1 = 2 and 6 is divisible by 2.

Mathematica

pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; pellNivenQ[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[pell[k] <= m, k++]; k--; AppendTo[s, k]; m -= pell[k]; k = 1]; Divisible[n, Plus @@ IntegerDigits[Total[3^(s - 1)], 3]]]; seq[count_, nConsec_] := Module[{pn = pellNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ pn, c++; AppendTo[s, k - nConsec]]; pn = Join[Rest[pn], {pellNivenQ[k]}]; k++]; s]; seq[30, 3]

Crossrefs

Cf. A000129, A265744, A317204.

A182190 \ {0} is a subsequence.

Subsequence of A352320 and A352321.

Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109.

Sequence in context: A201243 A092712 A202964 * A183469 A058227 A296392

Adjacent sequences: A352319 A352320 A352321 * A352323 A352324 A352325

Keyword

nonn,base

Author

Amiram Eldar, Mar 12 2022

Status

approved