A378808 -id:A378808 - cp's OEIS frontend

A378775 Prime numbers with monotonically decreasing digits, differing by at most 1.

2, 3, 5, 7, 11, 43, 211, 433, 443, 877, 887, 2111, 2221, 3221, 5443, 8887, 9887, 22111, 33211, 43321, 54443, 65543, 76543, 98887, 99877, 322111, 332221, 443221, 444443, 766543, 888887, 988877, 2221111, 3221111, 3222211, 3222221, 3333221, 4322221, 4433333, 4443221

Offset: 1

Randy L. Ekl, Dec 06 2024

			211 is a term since 211 is a prime number, the digits of 211 are monotonically decreasing, and the difference between consecutive digits is at most 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Primes in A378808.

Cf. A378774, A028864.

extend:= proc(x) local d,s,i;
  d:= ilog10(x);
  s:= floor(x/10^d);
  seq(10^(d+1)*i+x, i=s .. min(9,s+1))
end proc:
R:= 2,3,5,7: count:= 4:
M:= [1,3,7,9];
for d from 2 while count < 100 do
  M:= map(extend,M):
  S:= sort(select(isprime,M));
  count:= count+nops(S);
  R:= R,op(S);
od:
R; # Robert Israel, Feb 09 2025

Select[Prime[Range[312218]],ContainsOnly[Drop[IntegerDigits[#],-1]-Rest[IntegerDigits[#]],{0,1}]&] (* James C. McMahon, Dec 21 2024 *)

isok(p) = if (isprime(p), my(d=digits(p), dd = vector(#d-1, k, d[k+1]-d[k])); (#dd==0) || ((vecmin(dd)>=-1) && (vecmax(dd)<=0))); \\ Michel Marcus, Dec 09 2024

A378949 Numbers with monotonically increasing digits, increasing by only 0 or 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 22, 23, 33, 34, 44, 45, 55, 56, 66, 67, 77, 78, 88, 89, 99, 111, 112, 122, 123, 222, 223, 233, 234, 333, 334, 344, 345, 444, 445, 455, 456, 555, 556, 566, 567, 666, 667, 677, 678, 777, 778, 788, 789, 888, 889, 899, 999

Offset: 1

Randy L. Ekl, Dec 18 2024

			33 is a term since the digits are monotonically increasing and their difference is 0.
34 is also a term since the digits are monotonically increasing and their difference is 1.
35 is not a term since the difference in consecutive digits is not 0 or 1.
32 is not a term since the digits are decreasing.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A378808, A378774.

extend:= proc(k) local m,d;
  m:= 10^ilog10(k);
  d:= floor(k/m);
  if d = 1 then 10*m+k else (d-1)*10*m+k, d*10*m+k fi
end proc:
R:= $1..9:
A:= [R]:
for i from 2 to 5 do
  A:= map(extend,A);
  R:= R, op(sort(A));
od:
R; # Robert Israel, Jan 18 2025

Select[Range[1000],SubsetQ[{0, 1}, Union@ Differences@ IntegerDigits[#]] &] (* James C. McMahon, Dec 21 2024 *)

from itertools import count, islice
def bgen(last, d):
    if d == 0: yield tuple(); return
    t = (1, 9) if last == None else (last, min(last+1, 9))
    for i in range(t[0], t[1]+1): yield from ((i, )+r for r in bgen(i, d-1))
def agen(): # generator of terms
    yield from (int("".join(map(str, i))) for d in count(1) for i in bgen(None, d))
print(list(islice(agen(), 62))) # Michael S. Branicky, Dec 18 2024

Offset corrected by James C. McMahon, Dec 21 2024

cp's OEIS Frontend

A378775 Prime numbers with monotonically decreasing digits, differing by at most 1.

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