A305900 -id:A305900 - cp's OEIS frontend

A331300 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A057889(n)), and A057889 is a bijective base-2 reverse.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 19, 22, 25, 26, 23, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 34, 38, 39, 40, 41, 42, 43, 44, 32, 35, 45, 40, 39, 46, 47, 48, 36, 42, 47, 49, 43, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 57, 62, 69, 70, 71, 72, 73, 74, 65, 75, 76, 77, 78, 79, 80, 81, 55, 58, 82, 64, 69, 83, 84, 74, 63

Offset: 0

Antti Karttunen, Jan 18 2020

Restricted growth sequence transform of A331166. See comments in that sequence.

Antti Karttunen, Table of n, a(n) for n = 0..100000
Index entries for sequences related to binary expansion of n

Cf. A057889, A331166.

Cf. also A324400, A331303, A305801, A305801, A305900, A295300 for other "top level" filtering sequences.

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; };
A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A331166(n) = min(n, A057889(n));
v331300 = rgs_transform(vector(1+up_to,n,A331166(n-1)));
A331300(n) = v331300[1+n];
for(n=0,up_to,write("b331300.txt", n, " ", A331300(n)));

A374131 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n > 1, f(n) = [A083345(n), A374132(n), A374133(n)], where A083345 is the numerator of the fully additive function with a(p) = 1/p, and A374132 and A374133 are the 2- and 3-adic valuations of A276085, which is fully additive with a(p) = p#/p.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 30 2024

nonn

Restricted growth sequence transform of the function f given in the definition.
For all i, j >= 1:
  A305900(i) = A305900(j) => a(i) = a(j),
  a(i) = a(j) => A035263(i) = A035263(j),
  a(i) = a(j) => A369001(i) = A369001(j),
  a(i) = a(j) => A369004(i) = A369004(j),
  a(i) = a(j) => A372573(i) = A372573(j),
  a(i) = a(j) => A373137(i) = A373137(j),
  a(i) = a(j) => A373258(i) = A373258(j),
  a(i) = a(j) => A373483(i) = A373483(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A083345, A374132, A374133.
Cf. A035263, A305900, A369001, A369004, A372573, A373137, A373258, A373483.
Cf. also A373151.

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; };
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
Aux374131(n) = if(1==n, n, my(u=A276085(n)); [A083345(n), valuation(u, 2), valuation(u, 3)]);
v374131 = rgs_transform(vector(up_to, n, Aux374131(n)));
A374131(n) = v374131[n];

A305903 Filter sequence for all such sequences b, for which b(A014580(k)) = constant for all k >= 3.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 14 2018

nonn

Restricted growth sequence transform of A305900(A091203(n)).
This is GF(2)[X] analog of A305900.
For all i, j:
  a(i) = a(j) => A304529(i) = A304529(j) => A305788(i) = A305788(j).
  a(i) = a(j) => A268389(i) = A268389(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences operating on GF(2)[X]-polynomials

Cf. A091203, A268389, A278233, A304529, A305788, A305900.

up_to = 1000;
A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
prepare_v091226(up_to) = { my(v = vector(up_to), c=0); for(i=1,up_to,c += A091225(i); v[i] = c); (v); }
v091226 = prepare_v091226(up_to);
A091226(n) = if(!n,n,v091226[n]);
A305903(n) = if(n<7,n,if(A091225(n),7,3+n-A091226(n)));

For n < 7, a(n) = n, for >= 7, a(n) = 7 when n is in A014580[3..] (= 7, 11, 13, 19, 25, 31, ...), and a(n) = 3+n-A091226(n) when n is in A091242[4..] (= 8, 9, 10, 12, 14, 15, ...).

A319707 Filter sequence which records for primes their residue modulo 6, and for all other numbers assigns a unique number.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 04 2018

nonn

Restricted growth sequence transform of function f defined as f(n) = A010875(n) when n is a prime, otherwise -n.
Primes of the form 6k+5 (A007528) get value 5, and the primes of the form 6k+1 (A002476) get value 7, while for all other n, a(n) is assigned to a unique running count.
For all i, j:
  a(i) = a(j) => A010875(i) = A010875(j),
  a(i) = a(j) => A305900(i) = A305900(j),
  a(i) = a(j) => A319717(i) = A319717(j) => A319716(i) = A319716(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A319716, A319717.
Cf. A007528 (positions of 5's), A002476 (positions of 7's).
Cf. also A319704.
Differs from A319716 for the first time at n=121.

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; };
A319707aux(n) = if(isprime(n),(n%6),-n);
v319707 = rgs_transform(vector(up_to,n,A319707aux(n)));
A319707(n) = v319707[n];

A323161 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=3) = -n, f(n) = 0 if n-1 is an odd prime, and f(n) = floor((n-1)/2) for all other numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 4, 6, 4, 7, 7, 8, 4, 9, 4, 10, 10, 11, 4, 12, 4, 13, 13, 14, 4, 15, 15, 16, 16, 17, 4, 18, 4, 19, 19, 20, 20, 21, 4, 22, 22, 23, 4, 24, 4, 25, 25, 26, 4, 27, 27, 28, 28, 29, 4, 30, 30, 31, 31, 32, 4, 33, 4, 34, 34, 35, 35, 36, 4, 37, 37, 38, 4, 39, 4, 40, 40, 41, 41, 42, 4, 43, 43, 44, 4, 45, 45, 46, 46, 47, 4, 48, 48, 49, 49, 50, 50, 51, 4, 52, 52, 53, 4, 54, 4

Offset: 1

Antti Karttunen, Jan 06 2019

nonn

For all i, j: A322809(i) = A322809(j) <=> a(i+1) = a(j+1).
For all i, j: a(i) = a(j) => b(i) = b(j), where b can be, but is not limited to, any of the following sequences: A029834, A049084, A062590, A063377, A064891, A078442 (A049076), A175663, A175682, A269668, A292936, A323162, many of which are related to counting primes in certain kinds of chains or iterations.
Why does this work? Consider the function f given in the definition: based on its properties, we can deduce from the value of f(n) the following information about n:
  (A) If f(n) = -2, then n is 2, the only even prime,
  (B) If f(n) = -3, then n is 3, the first odd prime,
  (C) If f(n) is zero, then n is an even composite preceded by a prime, but we don't know which even composite exactly,
  (D) If f(n) > 0 and f(1+2*f(n)) = f(2+2*f(n)), then n is either (D1) an odd composite number, or (D2) an even composite number preceded by an odd composite number, and the said composite number in both cases is 1 + 2*f(n),
  (E) If f(n) > 0 and f(1+2*f(n)) <> f(2+2*f(n)), then n is an odd prime > 3, specifically, 1 + 2*f(n).
As this sequence is a restricted growth sequence transform of the said function f, we have a(i) = a(j) <=> f(i) = f(j) for all i, j, thus, even without knowing the value of n, but just a(n), we can find the value of f(n) by searching for the minimal k such that a(k) = a(n), then compute f(k) with that k. Furthermore, any function g defined as g(n) = h(f(n)) [where h is any function], clearly satisfies
  a(i) = a(j) => g(i) = g(j), for all i, j. [*]
For instances of such functions g, we can consider many sequences like those sequences b(n) listed above, that have g(n) = 0 for all composite numbers, and g(p) > 0 for all primes p. This is usually the pattern, but there are exceptions, like A323162, which is the characteristic function of A005381, composites n such that n-1 is also composite. These are precisely the numbers that occur twice in this sequence, while all other numbers (including primes), occur just once, that is, reside in their own singular equivalence classes. Thus, it is not guaranteed that all sequences g matching to this sequence (i.e. those satisfying the implication *), even if not false positives in strict sense, would necessarily have some consistent relation to primes, instead, they might contain any random values at the positions given by A093515. However, in the current OEIS, such sequences are exceedingly rare.

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A305801, A305900, A322809.
Cf. A005381 (numbers that occur twice in this sequence), A093515 (numbers > 1 that occur just once).
Cf. A010051, A029834, A049076, A049084, A062590, A063377, A064891, A078442, A175663, A175682, A269668, A292936, A323162 (some of the matched sequences).

up_to = 10000;
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; };
A323161aux(n) = if(n<=3,-n,if(isprime(n-1),0,((n-1)>>1))); \\ This implements the function f of the definition.
v323161 = rgs_transform(vector(up_to,n,A323161aux(n)));
A323161(n) = v323161[n];

a(1) = 1; for n > 1, a(n) = 1 + A322809(n-1).

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

Antti Karttunen, Dec 01 2022

nonn

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).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A007814, A007949, A046523, A065333, A072078, A305891, A305893, A322026.

Cf. also A358747.

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];

A373595 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A373591(n), A373592(n)].

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 13 2024

nonn

Restricted growth sequence transform of the function f given in the definition.
For all i, j > 1:
  A305900(i) = A305900(j) => A373594(i) = A373594(j) => a(i) = a(j),
  A373593(i) = A373593(j) => a(i) = a(j),
  a(i) = a(j) => b(i) = b(j), where b can be (but is not limited to) any of the sequences listed at the crossrefs-section, under "some of the matched sequences".

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A007949, A373591, A373592.
Cf. A305900, A373593, A373594.
Some of the matched sequences (see comments): A001222, A359430, A369643, A369658, A373371, A373383, A373474, A373491, A373493, A373585, A373588, A373596.

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; };
A007949(n) = valuation(n,3);
A373591(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%3)*n[2, i]);
A373592(n) = sum(i=1, #n=factor(n)~, (2==n[1, i]%3)*n[2, i]);
Aux373595(n) = if(n<=3, n, if(isprime(n), 0, [A007949(n), A373591(n), A373592(n)]));
v373595 = rgs_transform(vector(up_to, n, Aux373595(n)));
A373595(n) = v373595[n];

A305904 Filter sequence for all such sequences S, for which S(A091206(k)) = constant for all k >= 3, where A091206 gives primes whose binary representation encodes a polynomial irreducible over GF(2).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 7, 11, 7, 12, 13, 14, 15, 16, 7, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 7, 28, 29, 30, 31, 32, 7, 33, 34, 35, 7, 36, 37, 38, 39, 40, 7, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 7, 52, 7, 53, 54, 55, 56, 57, 7, 58, 59, 60, 61, 62, 7, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 7

Offset: 1

Antti Karttunen, Jun 16 2018

nonn

Restricted growth sequence transform of the ordered pair [A305900(n), A305903(n)].

For all i, j: a(i) = a(j) => A305815(i) = A305815(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences operating on GF(2)[X]-polynomials

Cf. A091206, A305815, A305816, A305817, A305900, A305903.

up_to = 100000;
A305816(n) = (isprime(n)&&polisirreducible(Pol(binary(n))*Mod(1,2)));
partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
v305817 = partialsums(A305816, up_to);
A305817(n) = v305817[n];
A305904(n) = if(n<7,n,if(A305816(n),7,3+n-A305817(n)));

For n < 7, a(n) = n; for >= 7, a(n) = 7 if A305816(n) = 1 [when n is in A091206[3..] = 7, 11, 13, 19, 31, 37, 41, ...], and 3+n-A305817(n) otherwise.

A358747 Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 2, 11, 12, 5, 13, 5, 14, 3, 2, 5, 15, 16, 2, 17, 4, 5, 6, 5, 18, 3, 2, 19, 20, 5, 2, 3, 21, 5, 22, 5, 4, 23, 2, 5, 24, 19, 25, 3, 4, 5, 26, 27, 28, 3, 2, 5, 10, 5, 2, 29, 30, 5, 6, 5, 4, 3, 31, 5, 32, 5, 2, 33, 4, 19, 6, 5, 34, 35, 2, 5, 36, 27, 2, 3, 7, 5, 13, 19, 4, 3, 2, 5, 37, 5, 38, 8, 14, 5, 6, 5, 7, 39

Offset: 1

Antti Karttunen, Dec 01 2022

For all i, j: A305900(i) = A305900(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A007814, A007949, A324198.

Cf. also A305900, A358230.

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);
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
Aux358747(n) = if(1==n,n,[A007814(n), A007949(n), A324198(n)]);
v358747 = rgs_transform(vector(up_to, n,Aux358747(n)));
A358747(n) = v358747[n];

A366296 Lexicographically earliest infinite sequence such that a(i) = a(j) => A346242(i) = A346242(j) for all i, j >= 1, where A346242 is Dirichlet inverse of gcd(n, A276086(n)).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 07 2023

nonn

Restricted growth sequence transform of A346242.

For all i, j: A305900(i) = A305900(j) => a(i) = a(j) => A008966(i) = A008966(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A008966, A276086, A305900, A324198, A346242.

Cf. also A366297.

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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
v366296 = rgs_transform(DirInverseCorrect(vector(up_to,n,A324198(n))));
A366296(n) = v366296[n];

cp's OEIS Frontend

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A319707 Filter sequence which records for primes their residue modulo 6, and for all other numbers assigns a unique number.

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A323161 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=3) = -n, f(n) = 0 if n-1 is an odd prime, and f(n) = floor((n-1)/2) for all other numbers.

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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.

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A373595 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A373591(n), A373592(n)].

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A305904 Filter sequence for all such sequences S, for which S(A091206(k)) = constant for all k >= 3, where A091206 gives primes whose binary representation encodes a polynomial irreducible over GF(2).

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A358747 Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1.

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