A378775 -id:A378775 - cp's OEIS frontend

A378774 Prime numbers with monotonically increasing digits, increasing by only 0 or 1.

2, 3, 5, 7, 11, 23, 67, 89, 223, 233, 677, 1123, 1223, 2333, 4567, 7789, 8999, 23333, 45667, 45677, 55667, 67777, 67789, 77899, 78889, 112223, 344567, 445567, 555677, 556789, 566677, 567899, 666667, 788999, 1112333, 2222333, 3445567, 3445667, 3455567, 3456667, 4455667, 4456789, 4556777

Offset: 1

Randy L. Ekl, Dec 06 2024

			223 is a term since the digits of 223 are monotonically increasing, consecutive digits differ by at most 1, and 223 is prime.

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

Cf. A028864, A378775.

extend:= proc(x) local d,s,i;
  d:= ilog10(x);
  s:= floor(x/10^d);
  seq(10^(d+1)*i+x, i=max(1,s-1) .. s)
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[319629]], ContainsOnly[Rest[IntegerDigits[#]]-Drop[IntegerDigits[#], -1], {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)>=0) && (vecmax(dd)<=1))); \\ Michel Marcus, Dec 09 2024

A378808 Numbers with monotonically decreasing digits, decreasing by only 0 or 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 32, 33, 43, 44, 54, 55, 65, 66, 76, 77, 87, 88, 98, 99, 100, 110, 111, 210, 211, 221, 222, 321, 322, 332, 333, 432, 433, 443, 444, 543, 544, 554, 555, 654, 655, 665, 666, 765, 766, 776, 777, 876, 877, 887, 888, 987, 988, 998, 999

Offset: 1

Randy L. Ekl, Dec 07 2024

			32 is a term since it has monotonically decreasing digits whose difference is at most 1.
33 is a term since it also has monotonically decreasing digits whose difference is at most 1.

Cf. A009996, A064222, A378775.

Select[Range[999],SubsetQ[{0,1},-Differences[IntegerDigits[#]]] &] (* Stefano Spezia, Dec 08 2024 *)

from itertools import count, islice
def bgen(last, d):
    if d == 0: yield tuple(); return
    t = (1, 9) if last == None else (max(0, last-1), last)
    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 08 2024

cp's OEIS Frontend

A378774 Prime numbers with monotonically increasing digits, increasing by only 0 or 1.

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