A336880 -id:A336880 - cp's OEIS frontend

A336954 Lexicographically earliest sequence of distinct positive terms such that, in the concatenation of the decimal representations of the terms, for any digit d at position p, d appears at some position q such that abs(p-q) = d.

1, 10, 2, 3, 20, 30, 4, 5, 6, 7, 40, 50, 60, 70, 8, 9, 11, 12, 32, 83, 90, 22, 220, 21, 13, 33, 333, 23, 24, 25, 34, 43, 52, 42, 26, 27, 28, 36, 63, 71, 18, 61, 14, 29, 240, 31, 130, 91, 15, 35, 53, 54, 55, 44, 37, 430, 41, 17, 45, 38, 93, 51, 16, 48, 49, 46

Offset: 1

Rémy Sigrist, Aug 08 2020

This sequence combines features of A322467 and of A336880.

Some numbers, like 121, cannot appear in this sequence.

			For n = 1:
- we can choose a(1) = 1.
For n = 2:
- a(2) must start with a digit 1,
- we can choose a(2) = 10.
For n = 3:
- we can choose a(3) = 2.
For n = 4:
- we can choose a(4) = 3.
For n = 5:
- a(5) must start with a digit 2,
- we can choose a(5) = 20.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A336954

Cf. A322467, A336880.

PARI
```
\\ See Links section.
```

A336905 Numbers n such that for any i > 0 there is some j > 0 such that the prime(i)-adic valuation of n, say x, equals the prime(j)-adic valuation of n and x = abs(i-j) (where prime(k) denotes the k-th prime number and the p-adic valuation of a number is the greatest m such that p^m divides that number).

Original entry on oeis.org

1, 6, 15, 30, 35, 77, 100, 105, 143, 210, 221, 323, 385, 437, 441, 462, 667, 858, 899, 1001, 1147, 1155, 1326, 1517, 1763, 1938, 2021, 2145, 2310, 2431, 2491, 2622, 2744, 3025, 3127, 3315, 3599, 4002, 4087, 4199, 4290, 4757, 4845, 5005, 5183, 5394, 5767, 6006

Offset: 1

Rémy Sigrist, Aug 07 2020

nonn

This sequence has connections with A336880.
All products of two successive prime numbers (A006094) belong to this sequence.
The product of two terms that are coprime is also a term.

			Regarding 14300:
- 14300 = 2^2 * 5^2 * 11 * 13 = prime(1)^2 * prime(3)^2 * prime(5) * prime(6),
- the 2-adic valuation is in correspondence with the 5-adic valuation,
- the 11-adic valuation is in correspondence with the 13-adic valuation,
- the p-adic valuation is in correspondence with itself for any prime number p that does not divide 14300,
- so 14300 is a term.

Cf. A006094, A336880.

is(n) = { my (f=factor(n), x=f[,2]~, pi=apply(primepi, f[,1]~), u, v); for (k=1, #x, if (((u=setsearch(pi, pi[k]-x[k])) && x[u]==x[k]) || ((v=setsearch(pi, pi[k]+x[k])) && x[v]==x[k]), "OK", return (0))); return (1) }

cp's OEIS Frontend

A336954 Lexicographically earliest sequence of distinct positive terms such that, in the concatenation of the decimal representations of the terms, for any digit d at position p, d appears at some position q such that abs(p-q) = d.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI