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Antti Karttunen, <a href="/A302853/b302853.txt">Table of n, a(n) for n = 0..30530</a>

Antti Karttunen: Looks quite regular/tame when compared to A304533.

Shares with sequences like A003188, A006068, A300838, A302846, A303765, A303767, A304083 and A304533 the property that when moving from any a(n) to a(n+1) either a subset of 0-bits are toggled on (changed to 1's), or a subset of 1-bits are toggled off (changed to 0's), but no both kind of changes may occur at the same step.

<a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

<a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

allocatedSuspected permutation forof Anttinonnegative Karttunenintegers: a(n) = A052331(A282291(1+n)).

0, 1, 3, 2, 6, 4, 12, 8, 9, 11, 10, 14, 30, 16, 17, 19, 18, 22, 20, 28, 24, 25, 27, 26, 31, 5, 7, 15, 13, 29, 21, 23, 87, 64, 65, 67, 66, 70, 68, 76, 72, 73, 75, 74, 78, 94, 80, 81, 83, 82, 86, 84, 92, 88, 89, 91, 90, 95, 69, 71, 79, 77, 93, 85, 117, 32, 33, 41, 40, 44, 36, 52, 48, 49, 57, 56, 60, 124, 96, 97, 105, 104, 108, 100, 116, 112, 113, 121, 120, 125

0,3

a(n) = A052331(A282291(1+n)).

(PARI)

up_to_e = 2^15;

v050376 = vector(up_to_e);

A050376(n) = v050376[n];

ispow2(n) = (n && !bitand(n, n-1));

i = 0; for(n=1, oo, if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e, break));

A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };

A302853(n) = A052331(A282291(1+n)); \\ Needs also code from A282291.

Cf. A302854 (inverse).

Cf. A052331, A282291.

Cf. also A304533.

allocated

nonn

Antti Karttunen, May 17 2018

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