A354150 -id:A354150 - cp's OEIS frontend

A354159 Terms 2*p (p prime) in A090252, divided by 2, in order of appearance.

2, 13, 103, 239, 499, 1567, 3257, 6971, 14447, 30259, 63317, 130699

Offset: 1

N. J. A. Sloane, May 30 2022

By definition, 2*a(n) is a term in A354255.

Conjecture: the indices of the terms 2*p in A090252 are terms in A083329.

			The indices in A090252 of the initial terms 2*p, the terms 2*p themselves, and the primes p are [5, 4, 2], [47, 26, 13], [767, 206, 103], [3071, 478, 239].

Cf. A083329, A090252, A354150, A354151, A354255.

a(6)-a(8) from Michael S. Branicky, Jun 04 2022 using A354255
a(9)-a(11) from Hugo van der Sanden, Jun 14 2022
a(12) from Jinyuan Wang, Jul 15 2022

A355893 Let A090252(n) = Product_{i >= 1} prime(i)^e(i); then a(n) is the concatenation, in reverse order, of e_1, e_2, ..., ending at the exponent of the largest prime factor of A090252(n); a(1)=0 by convention.

Original entry on oeis.org

0, 1, 10, 100, 2, 1000, 20, 10000, 100000, 1000000, 3, 10000000, 100000000, 200, 1010, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 4, 10000000000000000

Offset: 1

N. J. A. Sloane, Aug 23 2022

nonn

A090252 and A354169 are similar in many ways. This sequence and A355892 illustrate this.
This compressed format only make sense if all e_i are less than 10, that is, for n <= 24574.
It is believed that 6 does not appear in A090252, so 11 is missing from the present sequence.

			The initial terms of A090252 are:
1 -> 0
2 = 2^1 ->1
3 = 2^0 3^1 -> 10
5 = 2^0 3^0 5^1 -> 100
4 = 2^2 -> 2
7 = 2^0 3^0 5^0 7^1 -> 1000
9 = 2^0 3^2 -> 20
...
The terms, right-justified, for comparison with A355892, are:
.1 ...................................0
.2 ...................................1
.3 ..................................10
.4 .................................100
.5 ...................................2
.6 ................................1000
.7 ..................................20
.8 ...............................10000
.9 ..............................100000
10 .............................1000000
11 ...................................3
12 ............................10000000
13 ...........................100000000
14 .................................200
15 ................................1010
16 ..........................1000000000
17 .........................10000000000
18 ........................100000000000
19 .......................1000000000000
20 ......................10000000000000
21 .....................100000000000000
22 ....................1000000000000000
23 ...................................4
24 ...................10000000000000000
...

Michael De Vlieger, Table of n, a(n) for n = 1..1073

Cf. A054841, A090252, A354169.

See A354150 for indices of powers of 2 in A090252.

nn = 24, s = Import["https://oeis.org/A090252/b090252.txt", "Data"][[1 ;; nn, -1]]; f[n_] := If[n == 1, 0, Function[g, FromDigits@ Reverse@ ReplacePart[Table[0, {PrimePi[g[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, g]]@ FactorInteger@ n]; Array[f[s[[#]]] &, nn] (* Michael De Vlieger, Aug 24 2022 *)

a(n) = A054841(A090252(n)). - Stefano Spezia, Aug 24 2022

cp's OEIS Frontend

A354159 Terms 2*p (p prime) in A090252, divided by 2, in order of appearance.

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A355893 Let A090252(n) = Product_{i >= 1} prime(i)^e(i); then a(n) is the concatenation, in reverse order, of e_1, e_2, ..., ending at the exponent of the largest prime factor of A090252(n); a(1)=0 by convention.

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