A088629 Smallest number k not included earlier such that the concatenation n, k is a prime.

1, 3, 7, 19, 9, 13, 27, 11, 29, 21, 17, 23, 61, 33, 31, 37, 41, 47, 49, 39, 43, 51, 57, 59, 79, 63, 53, 87, 69, 67, 81, 71, 73, 91, 83, 77, 93, 89, 103, 99, 113, 97, 117, 101, 119, 133, 111, 109, 121, 123, 131, 127, 129, 139, 147, 149, 107, 151, 141, 161, 153, 137, 179

Offset: 1

Author

Amarnath Murthy, Oct 21 2003

Keywords

• base
• nonn

Comments

Another rearrangement of odd numbers not == 0 (mod 5).

Examples

			a(4) = 19. Though 41, 43 and 47 are prime 1, 3 and 7 have been included earlier and also 49, 411, 413 and 417 are not prime hence 419 is the required prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045572, A088630.

Programs

Python

from sympy import isprime
from itertools import count, islice
def agen():
    aset, mink = set(), 1
    for n in count(1):
        s, k = str(n), mink
        while k in aset or not isprime(int(s + str(k))): k += 1
        while mink%5 == 0 or mink in aset: mink += 2
        yield k; aset.add(k)
print(list(islice(agen(), 63))) # Michael S. Branicky, Aug 20 2022

Extensions

More terms from Ray G. Opao, Aug 19 2004