A360640 a(n) is the start of the least run of exactly n consecutive odd numbers that are A000120-perfect numbers (A175522).

25, 123, 31803, 8019811, 130194395

Offset

1,1

Comments

a(6) > 2*10^11, if it exists.

Links

Table of n, a(n) for n=1..5.

Example

Table of values of A000120 and A093653 for k = a(n), a(n)+2, ..., a(n)+2*(n-1):
  n |      a(n)              A000120(k)              A093653(k)
  --+----------------------------------------------------------
  1 |        25                       3                       6
  2 |       123                    6, 6.                 12, 12
  3 |     31803              10, 10, 11              20, 20, 22
  4 |   8019811          15, 15, 16, 15          30, 30, 32, 30
  5 | 130194395  17, 17, 18, 15, 16, 16  34, 34, 36, 30, 32, 32

Mathematica

q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] == 2 * DigitCount[n, 2, 1]; seq[len_, nmax_] := Module[{s = Table[0, {len}], v = {}, n = 1, c = 0, m}, While[c <= len && n <= nmax, If[q[n], v = Join[v, {n}], m = Length[v]; v = {}; If[0 < m <= len && s[[m]] == 0, c++; s[[m]] = n - 2*m]]; n += 2]; s]; seq[3, 10^5]

Prog

(PARI) lista(len, nmax) = {my(s = vector(len), v=[], n = 1, c = 0, m); while(c <= len && n <= nmax, if(sumdiv(n, d, hammingweight(d)) == 2 * hammingweight(n), v = concat(v, n), m =#v; v = []; if(0 < m && m <= len && s[m] == 0, c++; s[m] = n - 2*m)); n += 2); s};

Crossrefs

Cf. A000120, A093653, A175522, A360639.

Sequence in context: A087399 A030081 A075047 * A172047 A304422 A280390

Adjacent sequences: A360637 A360638 A360639 * A360641 A360642 A360643

Keyword

nonn,base,more

Author

Amiram Eldar, Feb 15 2023

Status

approved