A116068 Numbers k such that k has nondecreasing digits and the k-th prime has nonincreasing digits.

1, 2, 3, 4, 5, 11, 13, 14, 16, 18, 23, 25, 47, 67, 115, 116, 117, 119, 133, 135, 137, 147, 156, 166, 167, 168, 456, 566, 1166, 1167, 1168, 1178, 1179, 1199, 1225, 1226, 1229, 2479, 3566, 3569, 45567, 67999

Offset

1,2

Comments

No more terms < 200000. - Stefan Steinerberger, Mar 19 2006

No more terms < 10 million. - Harvey P. Dale, Sep 25 2014

No more terms < 1 billion. - Michael S. Branicky, Jun 27 2022

Links

Table of n, a(n) for n=1..42.

Example

prime(67999) = 855331.

Mathematica

For[n = 1, n < 70000, n++, a := IntegerDigits[n]; c := 0; For[m = 1, m <= Length[a] -1, m++, If[a[[m]] > a[[m + 1]], c := 1; ]]; If[c == 0, a:=IntegerDigits[Prime[n]]; For[m = 1, m <= Length[a] - 1, m++, If[a[[m]] < a[[m + 1]], c := 1; ]]]; If[c == 0, Print[n]]] (* Stefan Steinerberger, Mar 19 2006 *)
nddQ[n_]:=Min[Differences[IntegerDigits[n]]]>-1&&Max[Differences[ IntegerDigits[ Prime[ n]]]]<1; Select[Range[70000], nddQ] (* Harvey P. Dale, Sep 25 2014 *)

Prog

(Python)
from sympy import sieve
from itertools import count, islice, combinations_with_replacement as mc
def ni(n): s = str(n); return s == "".join(sorted(s, reverse=True))
def bgen(d): yield from map(int, ("".join(m) for m in mc("123456789", d)))
def agen():
    for d in count(1):
        yield from (k for k in bgen(d) if ni(sieve[k]))
print(list(islice(agen(), 42))) # Michael S. Branicky, Jun 26 2022

Crossrefs

Cf. A116066, A116067, A116069.

Sequence in context: A130640 A214653 A234142 * A104420 A188532 A181288

Adjacent sequences: A116065 A116066 A116067 * A116069 A116070 A116071

Keyword

nonn,base,more

Author

Giovanni Resta, Feb 13 2006

Status

approved