A278263 -id:A278263 - cp's OEIS frontend

A304113 Restricted growth sequence transform of A278263(n) = A046523(A064413(n)), a filter based on the prime signature of EKG-sequence.

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

Offset: 1

Antti Karttunen, May 17 2018

nonn

For all i, j: a(i) = a(j) => A064742(i) = A064742(j).

For all i, j: a(i) = a(j) => A065203(i) = A065203(j).

Antti Karttunen, Table of n, a(n) for n = 1..65539
Index entries for sequences related to EKG sequence

Cf. A046523, A064413, A064742, A065203, A278263, A304112.

Cf. also A304115.

\\ Needs also code for A064413:
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
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
A278263(n) = A046523(A064413(n));
write_to_bfile(1,rgs_transform(vector(65539,n,A278263(n))),"b304113.txt");

A304112 Restricted growth sequence transform of A246277(A064413(n)), related to indices in the prime factorization of EKG sequence.

Original entry on oeis.org

1, 2, 3, 4, 2, 3, 5, 6, 7, 2, 4, 8, 9, 2, 7, 10, 11, 12, 13, 2, 9, 6, 14, 3, 4, 15, 16, 2, 13, 17, 18, 19, 2, 16, 20, 21, 2, 19, 5, 22, 23, 24, 2, 21, 25, 26, 27, 28, 29, 3, 12, 30, 7, 9, 31, 32, 2, 24, 33, 34, 2, 32, 35, 36, 37, 38, 2, 34, 8, 39, 40, 41, 42, 2, 38, 11, 43, 4, 44, 45, 2, 42, 46, 13, 16, 47, 48, 49, 2, 45, 50, 51, 7

Offset: 1

Antti Karttunen, May 17 2018

nonn

For all i, j: a(i) = a(j) => A304113(i) = A304113(j).

Antti Karttunen, Table of n, a(n) for n = 1..65539
Index entries for sequences related to EKG sequence

Cf. A064413, A246277, A278263, A304113.

Cf. also A304114.

\\ Needs also code for A064413:
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
Aux304112(n) = A246277(A064413(n));
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
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(1,rgs_transform(vector(65539,n,Aux304112(n))),"b304112.txt");

A278264 Least number with the same prime signature as the n-th term in the inverse of EKG-sequence: a(n) = A046523(A064664(n)).

Original entry on oeis.org

1, 2, 2, 2, 6, 4, 6, 8, 6, 4, 12, 2, 12, 2, 2, 2, 6, 12, 2, 12, 6, 2, 2, 16, 24, 8, 6, 6, 6, 2, 2, 2, 6, 32, 4, 30, 2, 36, 2, 24, 6, 6, 16, 2, 6, 30, 2, 12, 12, 6, 6, 2, 36, 48, 2, 4, 6, 24, 2, 12, 6, 60, 6, 64, 24, 2, 128, 6, 12, 6, 6, 12, 30, 30, 6, 2, 30, 30, 2, 72, 12, 2, 96, 6, 60, 48, 6, 2, 2, 2, 6, 6, 6, 24, 6, 6, 30, 12, 96, 6, 24, 6, 2, 6, 2, 12, 6

Offset: 1

Antti Karttunen, Nov 16 2016

nonn

This sequence works as a "sentinel" for the inverse of EKG-sequence by matching to any other sequence that is obtained as f(A064664(n)), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ..."). As of Nov 11 2016 no such sequences were present in the database.

Terms and b-file computed from b-file of A064664 provided by T. D. Noe and Ray Chandler.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n

Cf. A046523, A064664, A278263.

(define (A278264 n) (A046523 (A064664 n)))

a(n) = A046523(A064664(n)).

cp's OEIS Frontend

A304113 Restricted growth sequence transform of A278263(n) = A046523(A064413(n)), a filter based on the prime signature of EKG-sequence.

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A304112 Restricted growth sequence transform of A246277(A064413(n)), related to indices in the prime factorization of EKG sequence.

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PARI

A278264 Least number with the same prime signature as the n-th term in the inverse of EKG-sequence: a(n) = A046523(A064664(n)).

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