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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A290076 Restricted growth sequence transform of A289625(A005940(1+n)).

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 4, 5, 4, 3, 6, 5, 7, 4, 8, 6, 9, 4, 10, 6, 11, 6, 11, 12, 13, 7, 14, 10, 15, 8, 16, 17, 18, 9, 19, 10, 14, 10, 20, 21, 22, 11, 23, 21, 24, 11, 25, 21, 26, 13, 27, 14, 28, 14, 24, 29, 30, 15, 31, 32, 33, 16, 34, 35, 36, 18, 11, 19, 37, 19, 22, 29, 38, 14, 39, 29, 40, 20, 41, 42, 24, 22, 43, 23, 44, 23, 45, 46, 47, 24, 44, 23, 48, 25
Offset: 0

Views

Author

Antti Karttunen, Jul 19 2017

Keywords

Comments

For all i, j: a(i) = a(j) => A290077(i) = A290077(j).

Links

Crossrefs

Cf. A005940, A289626, A290077, A290082.

Programs

  • PARI
    allocatemem(2^31);
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,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])); }
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
write_to_bfile(0,rgs_transform(vector(8193,n,A289625(A005940((1+n)-1)))),"b290076_upto8192.txt");

A296080 Restricted growth sequence transform of A289625(1+phi(n)), where phi = A000010, Euler totient function.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Dec 05 2017

Keywords

Links

Crossrefs

Cf. A000010, A039649, A289625, A289626, A296078.
Cf. A039650.

Programs

  • PARI
    allocatemem(2^30);
up_to = 65537;
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,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])); }
A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
write_to_bfile(1,rgs_transform(vector(up_to,n,A289625(1+eulerphi(n)))),"b296080.txt");

A303755 Ordinal transform of A289625.

Original entry on oeis.org

1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 2, 2, 1, 4, 1, 1, 1, 2, 1, 3, 1, 3, 2, 1, 1, 4, 1, 2, 3, 2, 1, 2, 2, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 3, 1, 5, 1, 2, 1, 2, 2, 2, 1, 6, 1, 1, 1, 2, 1, 3, 1, 3, 1, 1, 1, 7, 1, 2, 2, 2, 1, 1, 1, 4, 3, 3, 1, 4, 1, 1, 2
Offset: 1

Views

Author

Antti Karttunen, Apr 30 2018

Keywords

Comments

Equally, ordinal transform of A289626.

Links

Crossrefs

Cf. A289625, A289626.
Cf. also A081373, A303756.

Programs

  • PARI
    up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
v303755 = ordinal_transform(vector(up_to,n,A289625(n)));
A303755(n) = v303755[n];

A303712 a(n) is the smallest number such that there are exactly n numbers k (including a(n) itself) such that U(k) is isomorphic to U(a(n)) (or 0 if no such number exists). Here U(k) is the multiplicative group of integers modulo k.

Original entry on oeis.org

24, 1, 3, 7, 55, 129, 35, 104, 407, 707, 143, 371, 899, 665, 1144, 1771, 385, 3003, 3451, 5005, 7049, 8041, 7579, 12243, 4081, 5291, 3857, 9361, 2717, 2233
Offset: 1

Views

Author

Jianing Song, Apr 29 2018

Keywords

Comments

Conjecture: a(n) > 0 for all n.
Other known terms: a(35) = 8855, a(39) = 6149. [Corrected by Jianing Song, Oct 04 2018]
From Jianing Song, Oct 04 2018: (Start)
a(32) = 9269, a(33) = 7315, a(37) = 15953, a(52) = 16555, a(59) = 17081.
a(31), a(34), a(36), a(38) etc. > 2*10^4 (if not equal to 0). (End)

Examples

			U(24) is isomorphic to C_2 x C_2 x C_2 and there is no other number k such that U(k) is isomorphic to U(24), so a(1) = 24.
U(1) and U(2) are both isomorphic to the trivial group.
U(3), U(4) and U(6) are isomorphic to C_2.
U(7), U(9), U(14) and U(18) are isomorphic to C_6.
U(55), U(75), U(100), U(110) and U(150) are isomorphic to C_2 x C_20.
U(129), U(147), U(172), U(196), U(258) and U(294) are isomorphic to C_2 x C_42.
U(35), U(39), U(45), U(52), U(70), U(78) and U(90) are isomorphic to C_2 x C_12.
U(104), U(105), U(112), U(140), U(144), U(156), U(180) and U(210) are isomorphic to C_2 x C_2 x C_12.

Links

Crossrefs

Cf. A057635, A289626.

Programs

  • PARI
    b(n) = my(i=0, search_max = A057635(eulerphi(n))); for(j=eulerphi(n)+1, search_max, if(znstar(j)[2]==znstar(n)[2], i++)); i \\ search_max is the largest k such that phi(k) = phi(n). See A057635 for its program
a(n) = if(n==2, 1, my(t=3); while(b(t)!=n, t++); t) \\ Jianing Song, Oct 04 2018

Extensions

a(21)-a(24) from Jianing Song, Oct 04 2018
Previous Showing 11-14 of 14 results.

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