A375553 a(n) is the smallest prime q such that the concatenation (p + q)"q is a prime number, where p = prime(n).
3, 7, 3, 3, 19, 3, 31, 3, 3, 7, 11, 17, 3, 3, 3, 3, 13, 3, 29, 3, 23, 3, 3, 7, 41, 7, 3, 3, 3, 3, 3, 31, 7, 3, 3, 3, 11, 3, 7, 19, 3, 11, 7, 11, 3, 11, 3, 23, 7, 47, 19, 3, 23, 3, 7, 3, 7, 11, 3, 3, 11, 3, 23, 7, 3, 3, 3, 29, 7, 11, 7, 3, 11, 23, 3, 3, 3, 3, 13
Offset: 1
Links
- Sam Sweet, Table of n, a(n) for n = 1..500
Programs
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Maple
P := select(isprime, [seq(2..405)]): g := p -> local q; for q in P do if isprime(q + (p + q)*10^(1 + ilog10(q))) then return q fi od: map(g, P); -
Mathematica
spq[p_]:=Module[{k=2},While[!PrimeQ[(p+k)*10^IntegerLength[k]+k],k=NextPrime[k]];k]; Table[spq[p],{p,Prime[Range[80]]}] (* Harvey P. Dale, Sep 24 2024 *) -
PARI
a(n) = my(k=2); while (!isprime(eval(concat(Str(prime(n)+k), Str(k)))), k = nextprime(k+1)); k; \\ Michel Marcus, Sep 17 2024
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Python
from itertools import count from sympy import prime, isprime, nextprime def A375553(n): p, q, m = prime(n), 2, 10 for l in count(1): while q
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SageMath
def f(p): for q in Primes(): if is_prime(q + (p + q)*10^(1 + int(log(q, 10)))): return q print([f(p) for p in prime_range(405)])
Comments