A354839 Beginning with 0, smallest positive integer not yet in the sequence such that the concatenation of two digits of the sequence separated by a comma is prime.

0, 2, 3, 1, 7, 9, 70, 5, 30, 20, 21, 10, 22, 31, 11, 12, 32, 33, 13, 14, 15, 34, 16, 17, 18, 35, 36, 19, 71, 37, 38, 39, 72, 90, 23, 73, 74, 75, 91, 76, 77, 92, 93, 78, 94, 79, 700, 24, 100, 25, 95, 96, 101, 97, 98, 99, 701, 102, 300, 26, 103, 104, 105, 301

Offset

0,2

Links

Table of n, a(n) for n=0..63.

Example

a(4)=1 because this is the first number not in the sequence whose first digit is 3 (last digit of a(3)), concatenated with its first digit 1, is prime: 31.
a(14)=31 because this is the first number not in the sequence whose first digit is 2 (last digit of a(13)), concatenated with its first digit 3, is prime: 23.

Prog

(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    aset, k, mink = {0}, 0, 1; yield 0
    for n in count(2):
        k, prevdig = mink, str(k%10)
        while k in aset or not isprime(int(prevdig+str(k)[0])): k += 1
        aset.add(k); yield k
        while mink in aset: mink += 1
print(list(islice(agen(), 64))) # Michael S. Branicky, Jun 09 2022

Crossrefs

Cf. A074721, A158652, A152604-A152609, A152136, A152607.

Sequence in context: A118008 A256045 A173459 * A121637 A247370 A161847

Adjacent sequences: A354836 A354837 A354838 * A354840 A354841 A354842

Keyword

nonn,easy,base

Author

Carole Dubois, Jun 08 2022

Status

approved