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 A305932 Irregular table: row n >= 0 lists all k >= 0 such that the decimal representation of 2^k has n digits '0' (conjectured). 11
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 39, 49, 51, 67, 72, 76, 77, 81, 86, 10, 11, 12, 17, 20, 21, 22, 23, 26, 29, 30, 38, 40, 41, 44, 45, 46, 47, 48, 50, 57, 58, 65, 66, 68, 71, 73, 74, 75, 84, 85, 95, 96, 122, 124, 129, 130, 149, 151, 184, 43, 53, 61, 69, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A partition of the nonnegative integers (the rows being the subsets). Although it remains an open problem to provide a proof that the rows are complete (as are all terms of A020665), we can assume it for the purpose of this sequence. Read as a flattened sequence, a permutation of the nonnegative integers. LINKS M. F. Hasler, Zeroless powers.. OEIS Wiki, March 2014 FORMULA Row n = { k >= 0 | A027870(k) = n }. EXAMPLE The table reads: n \ k's 0 : 0, 1, ..., 9, 13, 14, 15, 16, 18, 19, 24, 25, 27, (...), 81, 86 (cf. A007377) 1 : 10, 11, 12, 17, 20, 21, 22, 23, 26, 29, 30, 38, 40, 41, 44, (...), 151, 184 2 : 42, 52, 54, 55, 56, 59, 60, 62, 63, 64, 78, 80, 82, 92, 107, (...), 171, 231 3 : 43, 53, 61, 69, 70, 83, 87, 89, 90, 93, 109, 112, 114, 115, (...), 221, 359 4 : 79, 91, 94, 97, 106, 118, 126, 127, 137, 139, 157, 159, 170, (...), 241, 283 5 : 88, 98, 99, 103, 104, 113, 120, 143, 144, 146, 152, 158, 160, (...), 343, 357 ... Column 0 is A031146: least k such that 2^k has n digits '0' in base 10. Row lengths = number of powers of 2 with exactly n '0's = (36, 41, 31, 34, 25, 32, 37, 23, 43, 47, 33, 35, 29, 27, 27, 39, 34, 34, 28, 29, ...): not in the OEIS. Largest number in row n = (86, 229, 231, 359, 283, 357, 475, 476, 649, 733, 648, 696, 824, 634, 732, 890, 895, 848, 823, 929, 1092, ...): not in OEIS Row number of n = Number of '0's in 2^n = A027870: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, ...) Inverse permutation (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 37, 38, 10, 11, 12, 13, 39, 14, 15, 40, 41, 42, 43, 16, 17, 44, 18, 19, 45, 46, 20, 21, ...) is not in OEIS. MATHEMATICA mx = 1000; g[n_] := g[n] = DigitCount[2^n, 10, 0]; f[n_] := Select[Range@mx, g@# == n &]; Table[f@n, {n, 0, 4}] // Flatten (* Robert G. Wilson v, Jun 20 2018 *) PROG (PARI) apply( A305932_row(n, M=200*(n+1))=select(k->A027870(k)==n, [0..M]), [0..20]) \\ A027870(k)=#select(d->!d, digits(2^k)) CROSSREFS Cf. A007377, A031146. Sequence A027870 yields the row number of a given integer. Cf. A305933 (analog for 3^n), A305924 (for 4^n), ..., A305929 (for 9^n). Sequence in context: A092598 A247811 A007377 * A213882 A135140 A052061 Adjacent sequences:  A305929 A305930 A305931 * A305933 A305934 A305935 KEYWORD nonn,base,tabf,nice AUTHOR M. F. Hasler, Jun 14 2018 STATUS approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)