A358931
a(n) is the smallest n-gonal pyramidal number with binary weight n.
Original entry on oeis.org
35, 30, 405, 95, 6860, 765, 28855, 7923, 96760, 380091, 259064, 915915, 3845501, 1436415, 32471830, 11992255, 62904941, 182171613, 266182382, 670936891, 939382515, 2533347310, 30530860911, 1876688877, 16972115903, 201845686175, 529756691451, 409027868651, 2713039388125
Offset: 3
405 is the smallest pentagonal pyramidal number with binary weight 5 (405_10 = 110010101_2), so a(5) = 405.
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p[n_, k_] := k*(k + 1)*((n - 2)*k + 5 - n)/6; a[n_] := Module[{k = 1, pk}, While[DigitCount[pk = p[n, k], 2, 1] != n, k++]; pk]; Array[a, 30, 3] (* Amiram Eldar, Dec 09 2022 *)
A358930
a(n) is the smallest n-gonal number with binary weight n.
Original entry on oeis.org
21, 169, 117, 190, 1404, 9976, 3961, 11935, 19966, 113401, 98155, 208879, 261501, 3338221, 916475, 3100671, 9943039, 31457140, 50322871, 100523871, 264240373, 2113871829, 2012739435, 532673535, 7415513007, 33017544153, 17112759966, 50983861215, 59039022015
Offset: 3
117 is the smallest pentagonal number with binary weight 5 (117_10 = 1110101_2), so a(5) = 117.
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p[n_, k_] := (n - 2)*k*(k - 1)/2 + k; a[n_] := Module[{k = 1, pk}, While[DigitCount[pk = p[n, k], 2, 1] != n, k++]; pk]; Array[a, 25, 3] (* Amiram Eldar, Dec 09 2022 *)
A359315
a(n) is the smallest centered triangular number with binary weight n.
Original entry on oeis.org
1, 10, 19, 46, 31, 235, 631, 1786, 1999, 7669, 7039, 12286, 16381, 180094, 114679, 949231, 2086831, 2883574, 4175839, 12480511, 50329585, 62898151, 132638719, 234618814, 771743710, 2883510271, 4269733885, 8254119871, 17045499901, 33214168831
Offset: 1
235 is the smallest centered triangular number with binary weight 6 (235_10 = 11101011_2), so a(6) = 235.
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seq[len_,nmax_] := Module[{s = Table[0,{len}], n = 1, c = 0, bw, ct}, While[c < len && n < nmax, bw = DigitCount[ct = 3*n*(n-1)/2 + 1, 2, 1]; If[bw <= len && s[[bw]] == 0, c++; s[[bw]] = ct]; n++]; s]; seq[30, 10^6] (* Amiram Eldar, Dec 26 2022 *)
A359316
a(n) is the smallest centered square number with binary weight n.
Original entry on oeis.org
1, 5, 13, 85, 61, 221, 761, 1013, 2813, 12013, 23545, 54781, 16381, 196565, 425965, 770041, 3137513, 7663613, 13629421, 20962813, 63946741, 121602013, 192805885, 499122013, 989724541, 2411720701, 6435110905, 17162301181, 29929502461, 63753420281
Offset: 1
221 is the smallest centered square number with binary weight 6 (221_10 = 11011101_2), so a(6) = 221.
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seq[len_,nmax_] := Module[{s = Table[0,{len}], n = 0, c = 0, bw, cs}, While[c < len && n < nmax, bw = DigitCount[cs = 2*n*(n+1) + 1, 2, 1]; If[bw <= len && s[[bw]] == 0, c++; s[[bw]] = cs]; n++]; s]; seq[30, 10^6] (* Amiram Eldar, Dec 26 2022 *)
Showing 1-4 of 4 results.