A379001 -id:A379001 - cp's OEIS frontend

A379005 Lexicographically earliest infinite sequence such that a(i) = a(j) => v_2(i) = v_2(j), v_3(i) = v_3(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814), v_3 (A007949) and v_5 (A112765) give the 2-, 3- and 5-adic valuations of n respectively.

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

Offset: 1

Antti Karttunen, Dec 15 2024

nonn

Restricted growth sequence transform of A355582.
For all i, j:
  A379001(i) = A379001(j) => a(i) = a(j),
  a(i) = a(j) => A322026(i) = A322026(j),
  a(i) = a(j) => A379004(i) = A379004(j).

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

Cf. A007814, A007949, A112765, A355582, A379006 (ordinal transform).

Cf. A322026, A379001, A379004.

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; };
v379005 = rgs_transform(vector(up_to, n, [valuation(n,2), valuation(n,3), valuation(n,5)]));
A379005(n) = v379005[n];

A379002 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A112765(i) = A112765(j), for all i, j, where A046523 gives the least representative of the prime signature of n and A112765 gives the 5-adic valuation of n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 15 2024

nonn

Restricted growth sequence transform of ordered pair [A046523(n), A112765(n)].
For all i, j:
  A379001(i) = A379001(j) => a(i) = a(j).

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

Cf. A046523, A112765, A379001.

Cf. also A305891, A305893.

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]); };
v379002 = rgs_transform(vector(up_to, n, [A046523(n), valuation(n,5)]));
A379002(n) = v379002[n];

A379000 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n is prime > 5, with f(n) = n for all other n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 15 2024

nonn

For all i, j:
  a(i) = a(j) => A305900(i) = A305900(j) => A305801(i) = A305801(j) => A305800(i) = A305800(j),
  a(i) = a(j) => A379001(i) = A379001(j) => A379002(i) = A379002(j),
  a(i) = a(j) => A379005(i) = A379005(j).

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

Cf. A000720.

Cf. A112765, A305800, A305801, A305900, A379001, A379002, A379005.

A379000(n) = if(n<=7, n, if(isprime(n), 7, 4+n-primepi(n)));

For n < 7, a(n) = n, for primes > 5, a(n) = 7, and for composite n > 7, a(n) = 4+n-A000720(n).

cp's OEIS Frontend

A379005 Lexicographically earliest infinite sequence such that a(i) = a(j) => v_2(i) = v_2(j), v_3(i) = v_3(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814), v_3 (A007949) and v_5 (A112765) give the 2-, 3- and 5-adic valuations of n respectively.

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A379002 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A112765(i) = A112765(j), for all i, j, where A046523 gives the least representative of the prime signature of n and A112765 gives the 5-adic valuation of n.

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A379000 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n is prime > 5, with f(n) = n for all other n.

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