A375552 Yet unseen terms in the enumeration of A375553, prepended by [2, 5].

2, 5, 3, 7, 19, 31, 11, 17, 13, 29, 23, 41, 47, 139, 61, 37, 53, 67, 59, 43, 89, 103, 109, 83, 73, 97, 79, 101, 71, 131, 167, 137, 107, 199, 163, 151, 191, 233, 113, 127, 227, 211, 179, 173, 239, 157, 193, 149, 181, 277, 313, 197, 223, 307, 251, 271, 331, 263, 241, 229, 349

Offset: 1

Author

Peter Luschny, Sep 17 2024

Keywords

• nonn

Comments

Conjecture: This is a permutation of the prime numbers.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..242

Crossrefs

Cf. A000040, A375553, A174414, A055642.

Programs

Maple

aList := proc(upto) local P, p, q, Y; Y := 2,5;
   P := select(isprime, [seq(2..upto)]):
   for p in P do for q in P do
      if isprime(q+(p+q)*10^(1+ilog10(q))) then break fi od:
   if not member(q, [Y]) then Y := Y,q fi od;
Y end: aList(100000);

Mathematica

spq[p_] := Module[{k = 2}, While[!PrimeQ[(p + k)*10^IntegerLength[k] + k], k = NextPrime[k]]; k];
Join[{2, 5}, DeleteDuplicates @ Table[spq[p], {p, Prime[Range[30000]]}]]
(* Jean-François Alcover, Oct 01 2024, after Harvey P. Dale in A375553 *)

PARI

f(n) = my(k=2); while (!isprime(eval(concat(Str(prime(n)+k), Str(k)))), k = nextprime(k+1)); k; \\ A375553
lista(nn) = my(list=List()); listput(list, 2); listput(list, 5); for (n=1, nn, my(k=f(n)); if (#select(x->(x==k), Vec(list)) == 0, listput(list, k));); Vec(list); \\ Michel Marcus, Sep 17 2024

Python

from itertools import count, islice
from sympy import isprime, nextprime
def A375552_gen(): # generator of terms
    p, a = 2, set()
    yield from (2,5)
    while True:
        q, m = 2, 10
        for l in count(1):
            while qA375552_list = print(list(islice(A375552_gen(),61))) # Chai Wah Wu, Sep 18 2024

SageMath

from more_itertools import unique_everseen
def f(p):
    for q in Primes():
        if is_prime(q + (p + q)*10^(1 + int(log(q, 10)))): return q
a = lambda n: unique_everseen((f(p) for p in prime_range(n)))
print([2, 5] + list(a(999)))