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 1-4 of 4 results.

A305900 Filter sequence for a(primes > 3) = constant sequences.

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, 59, 60, 5, 61, 62, 63, 5, 64, 65, 66, 67, 68, 5, 69, 70, 71, 72, 73, 74, 75, 5, 76
Offset: 1

Views

Author

Antti Karttunen, Jun 14 2018

Keywords

Comments

For all i, j:
a(i) = a(j) => A305801(i) = A305801(j) => A305800(i) = A305800(j).
a(i) = a(j) => A007949(i) = A007949(j).
a(i) = a(j) => A305893(i) = A305893(j).

Links

Crossrefs

Cf. A305800, A305801, A305893.
Cf. also A305901, A305902, A305903 (this filter applied to various permutations of N).

Programs

  • PARI
    A305900(n) = if(n<=5,n,if(isprime(n),5,3+n-primepi(n)));

Formula

For n <= 5, a(n) = n, for >= 5, a(n) = 5 when n is a prime, and a(n) = 3+n-A000720(n) when n is a composite.

A305891 Filter sequence combining 2-adic valuation (A007814) and the prime signature (A046523) of n.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 9, 10, 3, 11, 3, 8, 9, 5, 3, 12, 7, 5, 13, 8, 3, 14, 3, 15, 9, 5, 9, 16, 3, 5, 9, 12, 3, 14, 3, 8, 17, 5, 3, 18, 7, 11, 9, 8, 3, 19, 9, 12, 9, 5, 3, 20, 3, 5, 17, 21, 9, 14, 3, 8, 9, 14, 3, 22, 3, 5, 17, 8, 9, 14, 3, 18, 23, 5, 3, 20, 9, 5, 9, 12, 3, 24, 9, 8, 9, 5, 9, 25, 3, 11, 17, 16, 3, 14, 3, 12, 26, 5, 3, 27, 3
Offset: 1

Views

Author

Antti Karttunen, Jun 14 2018

Keywords

Comments

Restricted growth sequence transform of A286161, of the ordered pair [A007814(n), A046523(n)].
For all i, j: a(i) = a(j) => A291761(i) = A291761(j).

Links

Crossrefs

Cf. A286161, A291761, A305801.
Cf. also A305893.

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);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux305891(n) = [A007814(n), A046523(n)];
v305891 = rgs_transform(vector(up_to,n,Aux305891(n)));
A305891(n) = v305891[n];

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];

A379002 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A112765(i) = A112765(j), for all i, j, where A046523 gives the least representative of the prime signature of n and A112765 gives the 5-adic valuation of n.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 2, 6, 3, 7, 2, 8, 2, 5, 7, 9, 2, 8, 2, 10, 5, 5, 2, 11, 12, 5, 6, 8, 2, 13, 2, 14, 5, 5, 7, 15, 2, 5, 5, 16, 2, 17, 2, 8, 10, 5, 2, 18, 3, 19, 5, 8, 2, 11, 7, 11, 5, 5, 2, 20, 2, 5, 8, 21, 7, 17, 2, 8, 5, 13, 2, 22, 2, 5, 19, 8, 5, 17, 2, 23, 9, 5, 2, 24, 7, 5, 5, 11, 2, 20, 5, 8, 5, 5, 7, 25, 2, 8, 8, 26, 2, 17, 2, 11, 13
Offset: 1

Views

Author

Antti Karttunen, Dec 15 2024

Keywords

Comments

Restricted growth sequence transform of ordered pair [A046523(n), A112765(n)].
For all i, j:
A379001(i) = A379001(j) => a(i) = a(j).

Links

Crossrefs

Cf. A046523, A112765, A379001.
Cf. also A305891, A305893.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v379002 = rgs_transform(vector(up_to, n, [A046523(n), valuation(n,5)]));
A379002(n) = v379002[n];
Showing 1-4 of 4 results.

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