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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A269370 a(1) = 1, after which, for odd n: a(n) = A260439(n)-th number k for which A260438(k) = A260438(n)-1, and for even n: a(n) = a(n/2).

Original entry on oeis.org

1, 1, 2, 1, 4, 2, 3, 1, 7, 4, 6, 2, 9, 3, 13, 1, 8, 7, 5, 4, 15, 6, 10, 2, 21, 9, 19, 3, 12, 13, 25, 1, 31, 8, 14, 7, 33, 5, 11, 4, 16, 15, 37, 6, 27, 10, 18, 2, 43, 21, 49, 9, 20, 19, 45, 3, 39, 12, 22, 13, 17, 25, 51, 1, 24, 31, 63, 8, 67, 14, 26, 7, 69, 33, 73, 5, 28, 11, 75, 4, 23, 16, 30, 15, 55, 37, 79, 6, 32, 27, 61, 10, 87, 18, 34, 2
Offset: 1

Views

Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

For odd numbers n > 1, a(n) tells which term is on the immediately preceding row of A255551 (square array generated by Lucky sieve), in the same column where n itself is.

Links

Crossrefs

Cf. A255551, A260438, A260439, A269369.
Cf. also A268674, A269380.

Programs

Formula

a(1) = 1; after which for even n, a(n) = a(n/2), and for odd n, a(n) = A255551(A260438(n)-1, A260439(n)).
Other identities. For all n >= 1:
a(A269369(n)) = n.

A269863 Permutation of natural numbers: a(1) = 1, a(A269360(n)) = 2*a(n), a(A250469(1+n)) = 1 + 2*a(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 13, 18, 17, 26, 11, 12, 37, 34, 25, 74, 19, 20, 69, 50, 21, 14, 15, 16, 41, 138, 33, 82, 27, 36, 53, 22, 277, 66, 35, 52, 45, 554, 105, 90, 23, 24, 1109, 210, 101, 42, 75, 68, 49, 2218, 149, 38, 51, 148, 137, 98, 297, 274, 39, 40, 29, 30, 197, 594, 139, 100, 61, 394, 201, 122, 43, 28, 73, 106, 789, 402, 31, 32
Offset: 1

Views

Author

Antti Karttunen, Mar 13 2016

Keywords

Links

Crossrefs

Inverse: A269864.
Cf. A250469, A268674, A269360.
Differs from similarly constructed A245605 for the first time at n=21, where a(21)=19, instead of 15.

Formula

a(1) = 1, after which for even n, a(n) = 2*a(A268674(n-1)), for odd n, a(n) = 1 + 2*a(A268674(n)-1).

A302043 a(n) = n - A302042(n); an analog of A060681 based on the sieve of Eratosthenes (A083221).

Original entry on oeis.org

0, 1, 2, 2, 4, 3, 6, 4, 6, 5, 10, 6, 12, 7, 10, 8, 16, 9, 18, 10, 12, 11, 22, 12, 20, 13, 20, 14, 28, 15, 30, 16, 18, 17, 28, 18, 36, 19, 28, 20, 40, 21, 42, 22, 24, 23, 46, 24, 42, 25, 26, 26, 52, 27, 30, 28, 30, 29, 58, 30, 60, 31, 50, 32, 54, 33, 66, 34, 36, 35, 70, 36, 72, 37, 58, 38, 66, 39, 78, 40, 42, 41, 82, 42, 50, 43, 52, 44, 88, 45, 42
Offset: 1

Views

Author

Antti Karttunen, Mar 31 2018

Keywords

Comments

An analog of A060681 based on the sieve of Eratosthenes (A083221).

Links

Crossrefs

Cf. A060681, A302042.

Programs

Formula

a(n) = n - A302042(n).

A302046 A filter sequence analogous to A101296 for nonstandard factorization based on the sieve of Eratosthenes (A083221).

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 6, 2, 6, 5, 4, 2, 8, 3, 4, 4, 6, 2, 9, 2, 10, 6, 4, 4, 11, 2, 4, 4, 8, 2, 8, 2, 6, 7, 4, 2, 12, 3, 6, 6, 6, 2, 9, 5, 8, 6, 4, 2, 13, 2, 4, 4, 14, 4, 13, 2, 6, 8, 9, 2, 15, 2, 4, 4, 6, 4, 9, 2, 12, 6, 4, 2, 15, 6, 4, 9, 8, 2, 12, 5, 6, 10, 4, 4, 16, 2, 6, 4, 11, 2, 13, 2, 8, 11
Offset: 1

Views

Author

Antti Karttunen, Mar 31 2018

Keywords

Comments

Restricted growth sequence transform of A278524.
See A302042 for the description of the nonstandard factorization employed here.
For all i, j:
a(i) = a(j) => A253557(i) = A253557(j).
a(i) = a(j) => A302041(i) = A302041(j).
a(i) = a(j) => A302050(i) = A302050(j).
a(i) = a(j) => A302051(i) = A302051(j) => A302052(i) = A302052(j).

Links

Crossrefs

Cf. A101296, A250246, A278524, A302042, A302044, A302045.

Programs

  • PARI
    up_to = 32769;
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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A020639(n) = { if(1==n,n,vecmin(factor(n)[, 1])); };
A078898(n) = { if(n<=1,n, my(spf=A020639(n),k=1,m=n/spf); while(m>1,if(A020639(m)>=spf,k++); m--); (k)); };
A001511(n) = 1+valuation(n,2);
A302045(n) = A001511(A078898(n));
A302044(n) = if(1==n,n,my(k=0); while((n%2), n = A268674(n); k++); n = (n/2^valuation(n, 2)); while(k>0, n = A250469(n); k--); (n));
A302041(n) = if(1==n, 0,1+A302041(A302044(n)));
Aux302046(n) = if(1==n,n, my(k=A302041(n), v = vector(k),i=1); while(n>1,v[i] = A302045(n); n = A302044(n); i++); vecsort(v));
write_to_bfile(1,rgs_transform(vector(up_to,n,Aux302046(n))),"b302046.txt");

A269359 Self-inverse permutation of natural numbers: a(1)=1, a(A269360(n)) = A250469(1+a(n)), a(A250469(1+n)) = A269360(a(n)).

Original entry on oeis.org

1, 3, 2, 9, 6, 5, 26, 11, 4, 27, 8, 65, 66, 25, 16, 15, 120, 71, 36, 169, 76, 33, 74, 41, 14, 7, 10, 81, 86, 185, 206, 215, 22, 195, 50, 19, 330, 515, 196, 75, 24, 337, 186, 49, 46, 45, 348, 247, 44, 35, 358, 213, 116, 353, 290, 143, 106, 507, 536, 295, 1266, 1345, 226, 99, 12, 13, 512, 2321, 220, 123, 18, 1285, 306, 23, 40, 21
Offset: 1

Views

Author

Antti Karttunen, Mar 13 2016

Keywords

Links

Crossrefs

Cf. A250469, A268674, A269360.
Similar or related permutations: A244319, A269863, A269864, A269865, A269866, A269867.

Formula

a(1) = 1, after which for even n, a(n) = A250469(1+a(A268674(n-1))), for odd n, a(n) = A269360(a(A268674(n)-1)).
The declarative form can be expressed in terms of A250469 only:
a(1)=1, a(1+A250469(n)) = A250469(1+a(n)), a(A250469(1+n)) = 1+A250469(a(n)).
Previous Showing 21-25 of 25 results.

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