cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A336146 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A000265(i) = A000265(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, 42, 11, 43, 44, 45, 23, 46, 47, 48, 2, 49, 50, 51, 26, 52, 53, 54, 14, 55, 56, 57, 29, 58, 59, 60, 8, 61, 62, 63, 32, 64, 65, 66, 17, 67, 68, 69, 35, 70, 71, 72, 5, 73, 74, 75, 38, 76, 77, 78, 20, 79
Offset: 1

Views

Author

Antti Karttunen, Jul 12 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A000035(n), A000265(n)] (parity and the odd part of n), or equally, of the ordered pair [A000265(n), A278221(n)].
For all i, j:
A324400(i) = A324400(j) => a(i) = a(j),
a(i) = a(j) => A336126(i) = A336126(j),
a(i) = a(j) => A336147(i) = A336147(j),
a(i) = a(j) => A336148(i) = A336148(j),
a(i) = a(j) => A336149(i) = A336149(j).

Links

Crossrefs

Cf. A000035, A000265, A046523, A064989, A122111, A278221.
Cf. also A286621, A324400, A336126, A336147, A336148, A336149.

Programs

  • PARI
    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; };
A000035(n) = (n%2);
A000265(n) = (n>>valuation(n,2));
Aux336146(n) = [A000035(n), A000265(n)];
v336146 = rgs_transform(vector(up_to, n, Aux336146(n)));
A336146(n) = v336146[n];

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.

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, 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

Views

Author

Antti Karttunen, Jul 12 2020

Keywords

Comments

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).

Links

Crossrefs

Cf. A005940, A046523, A064989, A122111, A278221, A278222.
Cf. also A035531, A286621, A286622, A324400, A336146, A336148, A336159.

Programs

  • PARI
    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];

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

Views

Author

Antti Karttunen, Jul 12 2020

Keywords

Comments

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).

Links

Crossrefs

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.

Programs

  • PARI
    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];
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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