A116067 Numbers k such that both k and the k-th prime have nonincreasing digits.

1, 2, 3, 4, 5, 11, 20, 21, 64, 82, 83, 84, 86, 98, 100, 331, 720, 730, 732, 810, 821, 843, 921, 933, 940, 942, 970, 982, 983, 1100, 5540, 6442, 6542, 6644, 7331, 7411, 7433, 7440, 7442, 7443, 7511, 7520, 7530, 7531, 7620, 7630, 7641, 7642, 7644, 8210, 8500, 8510

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..82 (all terms < 10^8)

Example

prime(7531) = 76543.

Mathematica

Select[Range[9000], Max[Differences[IntegerDigits[#]]]< 1 && Max[ Differences[ IntegerDigits[ Prime[#]]]]<1&] (* Harvey P. Dale, Oct 11 2021 *)

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):
    ni = map(int, ("".join(m) for m in mc("9876543210", d)))
    yield from sorted(k for k in ni if k != 0)
def agen():
    for d in count(1):
        yield from (k for k in bgen(d) if ni(sieve[k]))
print(list(islice(agen(), 52))) # Michael S. Branicky, Jun 26 2022

Crossrefs

Cf. A116066, A116068, A116069.

Sequence in context: A121432 A118968 A073528 * A063685 A006481 A118597

Adjacent sequences: A116064 A116065 A116066 * A116068 A116069 A116070

Keyword

nonn,base

Author

Giovanni Resta, Feb 13 2006

Extensions

a(51) and beyond from Michael S. Branicky, Jun 26 2022

Status

approved