A118763 -id:A118763 - cp's OEIS frontend

A261725 Lexicographically earliest sequence of distinct terms such that the absolute difference of two successive terms is a power of 10, and can be computed without carry.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 60, 61, 62, 63, 64, 65, 66, 67

Offset: 0

Paul Tek, Aug 30 2015

In base 10, two successive terms have the same representation, except for one position, where the digits differ from exactly one unit. This difference can occur on a leading zero.
Conjectured to be a permutation of the nonnegative integers. See A261729 for putative inverse.
a(n) = A003100(n) for n < 101, but a(101) = 180, A003100(101) = 191.
a(n) = A118757(n) for n < 201, but a(201) = 281, A118757(201) = 290.
a(n) = A118758(n) for n < 100, but a(100) = 190, A118758(100) = 109.
a(n) = A174025(n) for n < 100, but a(100) = 190, A174025(100) = 199.
a(n) = A261729(n) for n < 100, but a(100) = 190, A261729(100) = 109.

Paul Tek, Table of n, a(n) for n = 0..10000
Paul Tek, PERL program for this sequence

Cf. A003100, A118757, A118763, A163252, A261729 (putative inverse).

Perl
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A372407 a(n) = smallest prime not occurring earlier having in decimal representation to its predecessor Levenshtein distance = 1.

Original entry on oeis.org

2, 3, 5, 7, 17, 11, 13, 19, 29, 23, 43, 41, 31, 37, 47, 67, 61, 71, 73, 53, 59, 79, 89, 83, 283, 223, 227, 127, 107, 101, 103, 109, 139, 131, 137, 157, 151, 181, 191, 193, 113, 163, 167, 197, 97, 397, 307, 317, 311, 211, 241, 251, 257, 277, 271, 281, 881, 811, 821, 421, 401, 409, 419, 439

Offset: 1

Eric Angelini and Giorgos Kalogeropoulos, Apr 29 2024

The sequence is a permutation of the prime numbers.

			The Levenshtein distance = 1 between 2 and 3, 3 and 5, 5 and 7, 7 and 17, 17 and 11, 11 and 13, etc.
No smaller prime than 17 was possible for a(5).

Eric Angelini, Prime combination lock, Personal blog, April 2024.

Cf. A000040, A118763, A372408.

a[1]=2;a[n_]:=a[n]=(k=2;While[MemberQ[Array[a,n-1],k]|| EditDistance[ToString@k, ToString@a[n-1]]!=1,k=NextPrime@k];k);Array[a,68]

from sympy import isprime
from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 2, {2}, 3
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 1 or not isprime(k): k += 1
        an = k
        aset.add(k)
        while mink in aset or not isprime(mink): mink += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Apr 29 2024

A372408 a(n) = smallest composite not occurring earlier having in decimal representation to its predecessor Levenshtein distance = 1; a(1)=1.

Original entry on oeis.org

1, 4, 6, 8, 9, 39, 30, 10, 12, 14, 15, 16, 18, 28, 20, 21, 22, 24, 25, 26, 27, 57, 50, 40, 42, 32, 33, 34, 35, 36, 38, 48, 44, 45, 46, 49, 69, 60, 62, 52, 51, 54, 55, 56, 58, 68, 63, 64, 65, 66, 76, 70, 72, 74, 75, 77, 78, 88, 80, 81, 82, 84, 85, 86, 87, 187, 117, 110, 100, 102, 104, 105, 106, 108, 118, 111, 112

Offset: 1

Eric Angelini and Giorgos Kalogeropoulos, Apr 29 2024

nonn

The sequence is a permutation of the nonprimes.

			The Levenshtein distance = 1 between 1 and 4, 4 and 6, 6 and 8, 8 and 9, 9 and 39, 39 and 30, 30 and 10, etc.
No smaller composite than 39 was possible for a(6).

Eric Angelini, Prime combination lock, Personal blog, April 2024.

Cf. A000040, A118763, A372407.

a[1]=1;a[n_]:=a[n]=(k=2;While[PrimeQ@k||MemberQ[Array[a,n-1],k]|| EditDistance[ToString@k,ToString@a[n-1]]!=1,k++];k);Array[a,77]

from sympy import isprime
from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 4
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 1 or isprime(k): k += 1
        an = k
        aset.add(k)
        while mink in aset or isprime(mink): mink += 1
print(list(islice(agen(), 80))) # Michael S. Branicky, Apr 29 2024

cp's OEIS Frontend

A261725 Lexicographically earliest sequence of distinct terms such that the absolute difference of two successive terms is a power of 10, and can be computed without carry.

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A372407 a(n) = smallest prime not occurring earlier having in decimal representation to its predecessor Levenshtein distance = 1.

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A372408 a(n) = smallest composite not occurring earlier having in decimal representation to its predecessor Levenshtein distance = 1; a(1)=1.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python