A357150 Primitive terms in A357148.
1, 3, 5, 7, 9, 15, 16, 24, 29, 32, 33, 34, 36, 42, 61, 64, 65, 72, 76, 82, 85, 91, 100, 104, 116, 127, 128, 129, 133, 144, 146, 153, 154, 169, 172, 179, 192, 209, 224, 256, 257, 258, 260, 262, 264, 270, 276, 281, 303, 322, 325, 339, 355, 356, 360, 400, 417, 418
Offset: 1
Keywords
Examples
Let b(n) = A357082(n). 3 is in the sequence since S = b(1) + b(2) = 1 + 2 = 3. Since b(3) = 3, it is not possible to see S = 3 again. 4 is not in the sequence since no sum S = 4 appears before b(4) = 4 = "100" in binary, whereafter "100" is appended to W, and thereafter prohibited as a sum of adjacent terms in b for n > 4. 32 is in the sequence since S = b(11) + b(12) = b(16) + b(17) = b(23) + b(24) = 32. We note that b(31) = 32, therefore these are the only instances of sum S = 32.
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Bitmap of a(n), n = 1..2^10, 6X vertical exaggeration, read horizontally where black represents 1 and white 0, with least significant bit on bottom.
- Scott R. Shannon, Image for n=1..28000.
Programs
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Mathematica
nn = 650; s[] = c[] = False; j = 0; i = u = 1; w = "0"; b = Reap[Do[k = u; While[Or[c[k], StringContainsQ[w, Set[v, IntegerString[j + k, 2]]]], k++]; c[k] = True; Sow[k]; If[! s[#], Set[{a[i], s[#]}, {#, True}]; i++] &[j + k]; Set[{j, w}, {k, w <> IntegerString[k, 2]}]; If[k == u, While[c[u], u++]], {n, nn}] ][[-1, -1]]; TakeWhile[Array[a, i - 1], MemberQ[b, #] &]