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 1-5 of 5 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.

A305973 Filter sequence for the prime signature of 2n-1.

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 2, 4, 2, 2, 4, 2, 3, 5, 2, 2, 4, 4, 2, 4, 2, 2, 6, 2, 3, 4, 2, 4, 4, 2, 2, 6, 4, 2, 4, 2, 2, 6, 4, 2, 7, 2, 4, 4, 2, 4, 4, 4, 2, 6, 2, 2, 8, 2, 2, 4, 2, 4, 6, 4, 3, 4, 5, 2, 4, 2, 4, 9, 2, 2, 4, 4, 4, 6, 2, 2, 6, 4, 2, 4, 4, 2, 8, 2, 3, 6, 2, 6, 4, 2, 2, 4, 4, 4, 9, 2, 2, 8, 2, 2, 4, 4, 4, 6, 4, 2, 4, 4, 4, 4, 4, 2, 10, 2, 2, 8, 2, 4, 4, 2
Offset: 1

Views

Author

Antti Karttunen, Jun 15 2018

Keywords

Comments

Restricted growth sequence transform of A278223, the least number with the same prime signature as the n-th odd number.

Links

Crossrefs

Cf. A046523, A101296, A278223, A305901, A305983, A305985.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
v305973 = rgs_transform(vector(up_to,n,A046523(n+n-1)));
A305973(n) = v305973[n];

A305810 Filter sequence for a(Sophie Germain primes > 3) = constant sequences.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 5, 22, 23, 24, 25, 26, 5, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 5, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 5, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 5, 78, 79, 80, 81, 82, 5, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 5
Offset: 1

Views

Author

Antti Karttunen, Jun 16 2018

Keywords

Comments

Filer sequence for all such sequences S, for which S(A005384(k)) = constant for all k >= 3.
Restricted growth sequence transform of the ordered pair [A305900(n), A305901(1+n)].
For all i, j:
a(i) = a(j) => A305900(i) = A305900(j),
a(i) = a(j) => A305901(1+i) = A305901(1+j),
a(i) = a(j) => A305978(i) = A305978(j),
a(i) = a(j) => A305985(i) = A305985(j).

Links

Crossrefs

Cf. A005384, A156660, A156874, A305900, A305901, A305978, A305985.

Programs

  • PARI
    up_to = 100000;
A156660(n) = (isprime(n)&&isprime(2*n+1)); \\ From A156660
partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
v156874 = partialsums(A156660, up_to);
A156874(n) = v156874[n];
A305810(n) = if(n<5,n,if(A156660(n),5,3+n-A156874(n)));

Formula

If n < 5, a(n) = n; for n >= 5, a(n) = 5 if A156660(n) == 1 [when n is in A005384[3..] = 5, 11, 23, 29, 41, 53, 83, 89, 113, ...], otherwise a(n) = 3+n-A156874(n).

A319706 Filter sequence which for primes p records the prime signature of 2p+1, and for all other numbers assigns a unique number.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 5, 6, 7, 8, 2, 9, 10, 11, 12, 13, 5, 14, 5, 15, 16, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 26, 27, 28, 29, 24, 30, 31, 32, 2, 33, 5, 34, 35, 36, 5, 37, 38, 39, 40, 41, 2, 42, 43, 44, 45, 46, 5, 47, 5, 48, 49, 50, 51, 52, 53, 54, 55, 56, 5, 57, 24, 58, 59, 60, 61, 62, 5, 63, 64, 65, 2, 66, 67, 68, 69, 70, 2, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 5
Offset: 1

Views

Author

Antti Karttunen, Sep 26 2018

Keywords

Comments

Restricted growth sequence transform of function f defined as f(n) = A046523(2n+1) when n is a prime, otherwise -n.
For all i, j:
A305810(i) = A305810(j) => a(i) = a(j),
and
a(i) = a(j) => A305800(i) = A305800(j),
a(i) = a(j) => A305978(i) = A305978(j),
a(i) = a(j) => A305985(i) = A305985(j).

Links

Crossrefs

Cf- A046523, A305800, A305810, A305900, A305901, A305978, A305985.
Cf. A005384 (positions of 2's), A234095 (positions of 5's).

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]); };  \\ From A046523
A319706aux(n) = if(isprime(n),A046523(n+n+1),-n);
v319706 = rgs_transform(vector(up_to,n,A319706aux(n)));
A319706(n) = v319706[n];

A305902 Restricted growth sequence transform of A305900(A048673(n)).

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 14 2018

Keywords

Comments

For all i, j:
a(i) = a(j) => A278224(i) = A278224(j).
a(i) = a(j) => A286583(i) = A286583(j).
a(i) = a(j) => A292251(i) = A292251(j).

Links

Crossrefs

Cf. A048673, A305900.
Cf. also A305901.

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; };
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A305900(n) = if(n<=5,n,if(isprime(n),5,3+n-primepi(n)));
v305902 = rgs_transform(vector(up_to,n,A305900(A048673(n))));
A305902(n) = v305902[n];
Showing 1-5 of 5 results.

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