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.

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A358230 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A007949(i) = A007949(j) and A046523(i) = A046523(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation, and A046523 gives the prime signature of its argument.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 9, 11, 12, 5, 13, 5, 14, 11, 9, 5, 15, 16, 9, 17, 14, 5, 18, 5, 19, 11, 9, 20, 21, 5, 9, 11, 22, 5, 18, 5, 14, 23, 9, 5, 24, 16, 25, 11, 14, 5, 26, 20, 22, 11, 9, 5, 27, 5, 9, 23, 28, 20, 18, 5, 14, 11, 29, 5, 30, 5, 9, 31, 14, 20, 18, 5, 32, 33, 9, 5, 27, 20, 9, 11, 22, 5, 34, 20, 14, 11, 9, 20, 35, 5, 25, 23, 36, 5, 18, 5, 22, 37
Offset: 1

Views

Author

Antti Karttunen, Dec 01 2022

Keywords

Comments

Restricted growth sequence transform of the triple [A007814(n), A007949(n), A046523(n)].
For all i, j:
A305900(i) = A305900(j) => a(i) = a(j),
a(i) = a(j) => A305891(i) = A305891(j),
a(i) = a(j) => A305893(i) = A305893(j),
a(i) = a(j) => A322026(i) = A322026(j) => A072078(i) = A072078(j),
a(i) = a(j) => A065333(i) = A065333(j).

Links

Crossrefs

Cf. A007814, A007949, A046523, A065333, A072078, A305891, A305893, A322026.
Cf. also A358747.

Programs

  • PARI
    up_to = 100000;
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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
v358230 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n), A046523(n)]));
A358230(n) = v358230[n];

A353277 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A020639(n), A341353(n)], with f(1) = 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 2, 6, 2, 7, 8, 9, 2, 10, 2, 3, 4, 11, 2, 12, 2, 13, 4, 14, 2, 15, 2, 3, 2, 16, 4, 17, 2, 3, 4, 5, 18, 19, 2, 7, 4, 20, 2, 21, 2, 3, 18, 22, 2, 23, 2, 3, 2, 24, 2, 25, 2, 7, 2, 26, 2, 27, 4, 3, 8, 5, 4, 28, 2, 3, 2, 29, 2, 30, 2, 3, 2, 6, 2, 31, 2, 7, 4, 32, 4, 15, 2, 33, 18, 34, 8, 35, 2, 3, 8, 5, 2
Offset: 1

Views

Author

Antti Karttunen, Apr 10 2022

Keywords

Comments

Restricted growth sequence transform of function f(1) = 1, and for n > 1, f(n) = [A007814(u), A007949(u)], where u = A156552(n).

Links

Crossrefs

Cf. A007814, A007949, A020639, A156552, A341353, A353278 (ordinal transform).
Cf. also A322026, A340680, A341355.

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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
Aux353277(n) = if(1==n,1,my(u=A156552(n)); [A007814(u), A007949(u)]);
v353277 = rgs_transform(vector(up_to, n, Aux353277(n)));
A353277(n) = v353277[n];

A374040 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A007814(n), A007949(n)], for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jul 01 2024

Keywords

Comments

Restricted growth sequence transform of the quadruple [A003415(n), A085731(n), A007814(n), A007949(n)].
For all i, j >= 1:
A305900(i) = A305900(j) => a(i) = a(j),
a(i) = a(j) => A322026(i) = A322026(j),
a(i) = a(j) => A369051(i) = A369051(j) => A083345(i) = A083345(j),
a(i) = a(j) => b(i) = b(j), where b can be any of the sequences listed at the crossrefs-section, under "some of the other matched sequences".

Links

Crossrefs

Cf. A003415, A007814, A007949, A085731.
Some of the other matched sequences (see comments): A083345, A359430, A369001, A369004, A369643, A369658, A373143, A373474, A373483.
Cf. also A322026, A353521, A369051, A373268, A372573, A374131 for similar and related constructions.
Differs from A305900 first at n=77, where a(77) = 50, while A305900(77) = 59.

Programs

  • PARI
    up_to = 100000;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
Aux374040(n) = { my(d=A003415(n)); [d, gcd(n,d), valuation(n,2), valuation(n,3)]; };
v374040 = rgs_transform(vector(up_to, n, Aux374040(n)));
A374040(n) = v374040[n];
Previous Showing 11-13 of 13 results.

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