A336146 -id:A336146 - cp's OEIS frontend

A336149 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A278222(i) = A278222(j), for all i, j >= 1.

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 38, 39, 20, 40, 41, 42, 11, 43, 44, 45, 23, 46, 47, 48, 2, 49, 50, 51, 26, 52, 53, 54, 14, 55, 56, 34, 29, 57, 58, 59, 8, 60, 61, 62, 32, 63, 64, 65, 17, 66, 67, 68, 35, 69, 70, 71, 5, 72, 27, 73, 38, 74, 75, 76, 20, 77

Offset: 1

Antti Karttunen, Jul 12 2020

nonn

Restricted growth sequence transform of the ordered pair [A278221(n), A278222(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A005940(1+n))].

For all i, j: A336146(i) = A336146(j) => a(i) = a(j) => A035531(i) = A035531(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A005940, A046523, A064989, A122111, A278221, A278222.

Cf. also A035531, A286621, A286622, A324400, A336146, A336148, A336159.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A278222(n) = A046523(A005940(1+n));
Aux336149(n) = [A278221(n),A278222(n)];
v336149 = rgs_transform(vector(up_to, n, Aux336149(n)));
A336149(n) = v336149[n];

A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 38, 39, 20, 40, 41, 25, 11, 42, 43, 44, 23, 45, 46, 47, 2, 48, 49, 50, 26, 51, 32, 52, 14, 53, 54, 34, 29, 55, 56, 57, 8, 58, 59, 60, 32, 61, 62, 63, 17, 64, 65, 30, 35, 66, 67, 68, 5, 69, 70, 71, 38, 72, 73, 74, 20, 75

Offset: 1

Antti Karttunen, Jul 12 2020

nonn

Restricted growth sequence transform of the ordered pair [A278221(n), A336158(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A000265(n))].

For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A046523, A064989, A122111, A278221, A336158.

Cf. also A286621, A318890, A324400, A336146, A336149, A336159.

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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A000265(n) = (n>>valuation(n,2));
A336158(n) = A046523(A000265(n));
Aux336148(n) = [A278221(n),A336158(n)];
v336148 = rgs_transform(vector(up_to, n, Aux336148(n)));
A336148(n) = v336148[n];

A336147 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 3, 7, 8, 5, 9, 10, 11, 2, 12, 5, 13, 7, 14, 15, 16, 5, 4, 17, 3, 10, 18, 19, 20, 2, 21, 22, 23, 5, 24, 25, 26, 7, 27, 28, 29, 15, 11, 30, 31, 5, 6, 7, 32, 17, 33, 5, 34, 10, 35, 36, 37, 19, 38, 39, 14, 2, 40, 41, 42, 22, 43, 28, 44, 5, 45, 46, 11, 25, 47, 48, 49, 7, 3, 50, 51, 28, 52, 53, 54, 15, 55, 19, 56, 30, 57, 58, 59, 5, 60, 10, 21, 7, 61, 62, 63, 17, 64

Offset: 1

Antti Karttunen, Jul 12 2020

nonn

Restricted growth sequence transform of the ordered pair [A020639(n), A278221(n)].
For all i, j:
  A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j),
  a(i) = a(j) => A243055(i) = A243055(j),
  a(i) = a(j) => A336150(i) = A336150(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A020639, A046523, A122111, A278221.
Cf. also A243055, A286621, A318891, A324400, A336146, A336148, A336149, A336150.
First differs from A322590 at a(70) = 28 instead of 44.

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; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
Aux336147(n) = [A020639(n),A278221(n)];
v336147 = rgs_transform(vector(up_to, n, Aux336147(n)));
A336147(n) = v336147[n];

A336126 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A007814(1+A000265(i)) = A007814(1+A000265(j)), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 6, 7, 2, 1, 2, 3, 2, 1, 4, 5, 4, 1, 2, 3, 6, 1, 8, 9, 2, 1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 6, 7, 4, 1, 2, 3, 2, 1, 4, 5, 6, 1, 2, 3, 8, 1, 10, 11, 2, 1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 6, 7, 2, 1, 2, 3, 2, 1, 4, 5, 4, 1, 2, 3, 6, 1, 8, 9, 4, 1, 2, 3, 2, 1, 4, 5, 2, 1

Offset: 1

Antti Karttunen, Jul 13 2020

nonn

Restricted growth sequence transform of the ordered pair [A000035(n), A007814(1+A000265(n))], parity and the number of trailing 1-bits in the odd part of n (i.e., the length of the rightmost run of 1-bits in its binary expansion).

For all i, j: A336146(i) = A336146(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A000265, A007814, A336146.

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; };
A000265(n) = (n>>valuation(n,2));
A007814(n) = valuation(n,2);
Aux336126(n) = [(n%2),A007814(1+A000265(n))];
v336126 = rgs_transform(vector(up_to, n, Aux336126(n)));
A336126(n) = v336126[n];

A336474 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A329697(i) = A329697(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 12, 38, 20, 39, 40, 25, 11, 41, 42, 43, 23, 44, 45, 46, 2, 47, 48, 49, 26, 50, 32, 51, 14, 52, 53, 34, 29, 54, 55, 56, 8, 57, 58, 59, 32, 60, 61, 62, 17, 63, 64, 65, 35, 66, 67, 68, 5, 69, 70, 71, 12, 72, 73, 74, 20, 75

Offset: 1

Antti Karttunen, Jul 25 2020

nonn

Restricted growth sequence transform of the ordered pair [A278221(n), A329697(n)].

For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A046523, A122111, A278221, A329697.

Cf. also A324400, A336146, A336473.

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; };
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336474(n) = [A278221(n), A329697(n)];
v336474 = rgs_transform(vector(up_to,n,Aux336474(n)));
A336474(n) = v336474[n];

cp's OEIS Frontend

A336149 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A278222(i) = A278222(j), for all i, j >= 1.

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A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336147 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

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A336126 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A007814(1+A000265(i)) = A007814(1+A000265(j)), for all i, j >= 1.

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A336474 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A329697(i) = A329697(j), for all i, j >= 1.

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