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A367697
Starts of runs of 15 consecutive integers that are exponentially odious numbers (A270428).
2
9, 73, 137, 169, 201, 393, 521, 553, 633, 649, 713, 761, 809, 841, 889, 1001, 1033, 1065, 1129, 1145, 1193, 1225, 1273, 1289, 1353, 1385, 1513, 1545, 1577, 1609, 1657, 1769, 1785, 1865, 1897, 1929, 2025, 2089, 2169, 2217, 2297, 2345, 2377, 2409, 2441, 2505, 2569
OFFSET
1,1
COMMENTS
The maximal length of a run of consecutive exponentially odious numbers is 15 since numbers of the form 16*k + 8 are not exponentially odious. Thus all the terms of this sequence are of the form 16*k + 9 with k = 0, 4, 8, 10, 12, 24, 32, 34, 39, 40, ... .
The numbers of terms not exceeding 10^k for k = 1, 2, ... , are 1, 2, 15, 176, 1821, 18120, 181277, 1812917, 18129256, 181290721, ... . Apparently, the asymptotic density of this sequence exists and equals 0.018129... .
LINKS
MATHEMATICA
expOdQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ[DigitCount[#, 2, 1]] &]; q[n_] := AllTrue[16*n + Range[9, 23], expOdQ]; 16 * Select[Range[0, 160], q] + 9
PROG
(PARI) isexpod(n) = {my(f = factor(n)); for(i=1, #f~, if (!(hammingweight(f[i, 2]) % 2), return (0))); 1; }
is(n) = {my(k = (n-9)/16); if(denominator(k) > 1, return(0)); for(i=9, 23, if(!isexpod(16*k + i), return(0))); 1; }
CROSSREFS
Subsequence of A270428 and A367696.
Similar sequences: A007675, A194002, A325058, A328016.
Sequence in context: A218126 A133672 A043079 * A099973 A091986 A096129
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Nov 27 2023
STATUS
approved