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
Examples
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
Programs
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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] -
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};
Comments