A344182 -id:A344182 - cp's OEIS frontend

A344026 Arithmetic derivative applied to the Doudna sequence: a(n) = A003415(A005940(1+n)).

0, 1, 1, 4, 1, 5, 6, 12, 1, 7, 8, 16, 10, 21, 27, 32, 1, 9, 10, 24, 12, 31, 39, 44, 14, 45, 55, 60, 75, 81, 108, 80, 1, 13, 14, 32, 16, 41, 51, 68, 18, 59, 71, 92, 95, 123, 162, 112, 22, 77, 91, 140, 119, 185, 240, 156, 147, 275, 350, 216, 500, 297, 405, 192, 1, 15, 16, 48, 18, 61, 75, 92, 20, 87, 103, 124, 135, 165, 216

Offset: 0

Antti Karttunen, May 07 2021

Coincides with A344028 on Fibbinary numbers, A003714.

Antti Karttunen, Table of n, a(n) for n = 0..8192
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A000079 (positions of ones), A003415, A003714, A005940.

Cf. also A344027, A344028, A344182.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344026(n) = A003415(A005940(1+n));

a(2^n) = 1 for all n >= 0.

A344028 a(n) = A069359(A005940(1+n)).

Original entry on oeis.org

0, 1, 1, 2, 1, 5, 3, 4, 1, 7, 8, 10, 5, 15, 9, 8, 1, 9, 10, 14, 12, 31, 24, 20, 7, 35, 40, 30, 25, 45, 27, 16, 1, 13, 14, 18, 16, 41, 30, 28, 18, 59, 71, 62, 60, 93, 72, 40, 11, 63, 70, 70, 84, 155, 120, 60, 49, 175, 200, 90, 125, 135, 81, 32, 1, 15, 16, 26, 18, 61, 42, 36, 20, 87, 103, 82, 80, 123, 90, 56, 24, 113, 131

Offset: 0

Antti Karttunen, May 11 2021

Coincides with A344026 on Fibbinary numbers, A003714.

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A000079 (positions of ones), A003714, A005940, A069359, A344026, A344182.

A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344028(n) = A069359(A005940(1+n));

a(n) = A069359(A005940(1+n)).

A344180 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 0, where f(n) = 0 if n is a Fibbinary number (A003714), otherwise f(n) = n.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 1, 5, 6, 7, 8, 9, 1, 1, 1, 10, 1, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1, 21, 1, 1, 22, 23, 1, 1, 1, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 1, 1, 1, 45, 1, 1, 46, 47, 1, 1, 1, 48, 49, 50, 51, 52, 1, 1, 1, 53, 1, 1, 54, 55, 56, 57

Offset: 0

Antti Karttunen, May 16 2021

nonn

For all i, j:
  a(i) = a(j) => A085357(i) = A085357(j),
  a(i) = a(j) => A213370(i) = A213370(j),
  a(i) = a(j) => A344182(i) = A344182(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A003714 (positions of 1's), A085357, A213370, A344182.

Cf. also A324400.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
Aux344180(n) = if(!bitand(n,n+n),0,n);
v344180 = rgs_transform(vector(1+up_to,n,Aux344180(n-1)));
A344180(n) = v344180[1+n];

cp's OEIS Frontend

A344026 Arithmetic derivative applied to the Doudna sequence: a(n) = A003415(A005940(1+n)).

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A344028 a(n) = A069359(A005940(1+n)).

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A344180 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 0, where f(n) = 0 if n is a Fibbinary number (A003714), otherwise f(n) = n.

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