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

Author

Randy L. Ekl, Dec 06 2024

Keywords

• nonn
• base
• look

Examples

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

Links

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

Crossrefs

Cf. A028864, A378775.

Programs

Maple

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

Mathematica

Select[Prime[Range[319629]], ContainsOnly[Rest[IntegerDigits[#]]-Drop[IntegerDigits[#], -1], {0, 1}]&] (* James C. McMahon, Dec 21 2024 *)

PARI

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