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

1,1

Links

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

Example

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.

Maple

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

Mathematica

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

Prog

(PARI) 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

Crossrefs

Primes in A378808.

Cf. A378774, A028864.

Sequence in context: A232183 A289862 A036343 * A058253 A004089 A092791

Adjacent sequences: A378772 A378773 A378774 * A378776 A378777 A378778

Keyword

nonn,base,look

Author

Randy L. Ekl, Dec 06 2024

Status

approved