A342874 Numbers k such that the k-th and (k+1)-st primes have the same digits.

293, 2106, 2161, 2763, 3698, 3793, 3812, 3922, 3959, 4000, 4205, 4224, 4260, 4728, 4953, 5065, 5283, 5617, 5700, 5751, 5932, 6326, 6333, 6422, 6539, 6623, 7375, 7475, 7501, 7533, 7542, 8306, 8568, 8751, 8777, 8994, 9102, 9259, 9354, 9480, 10389, 10700, 10791

Offset

1,1

Comments

Subsequence of A109182.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

prime(293) = 1913, while prime(294) = 1931. Thus, 293 is in this sequence.

Maple

q:= n-> (f-> is(f(n)=f(n+1)))(t-> sort(convert(ithprime(t), base, 10))):
select(q, [$1..15000])[];  # Alois P. Heinz, Mar 28 2021

Mathematica

Select[Range[10000], Sort[IntegerDigits[Prime[#]]] == Sort[IntegerDigits[Prime[# + 1]]] &]

Prog

(PARI) upto(n) = {my(t = 1, res = List(), q = 2); forprime(p = 3, oo, if((p - q)%9 == 0 && vecsort(digits(q)) == vecsort(digits(p)), listput(res, t); ); q = p; t++; if(t > n, return(res) ) ) } \\ David A. Corneth, Mar 29 2021
(Python)
from sympy import nextprime
from itertools import count, islice
def agen():
    p, pdigs, q, qdigs = 2, ["2"], 3, ["3"]
    for k in count(1):
        if pdigs == qdigs: yield k
        p, q = q, nextprime(q)
        pdigs, qdigs = qdigs, sorted(str(q))
print(list(islice(agen(), 43))) # Michael S. Branicky, Nov 27 2022

Crossrefs

Cf. A109182.

Sequence in context: A109562 A023305 A109182 * A241047 A085502 A108828

Adjacent sequences: A342871 A342872 A342873 * A342875 A342876 A342877

Keyword

nonn,base

Author

Tanya Khovanova, Mar 28 2021

Status

approved