|
|
A231432
|
|
Primes p such that abs(p - 3*k) is also prime, where p is the k-th prime.
|
|
1
|
|
|
3, 7, 13, 19, 31, 41, 47, 53, 61, 71, 79, 89, 101, 107, 113, 139, 151, 173, 193, 199, 223, 229, 239, 251, 271, 281, 293, 349, 373, 397, 433, 457, 463, 521, 541, 557, 569, 593, 601, 613, 619, 641, 647, 673, 683, 743, 787, 809, 839, 911, 941, 953, 971, 1013, 1049
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
The first prime, 2, is not a term since |2-3*1| = 1.
The second prime, 3, is a term, since |3-2*3| = 3 is a prime.
a(11) = 79 which is the 22nd prime, prime(22)-3*22 = 79-66 = 13 which is also prime.
a(15) = 113 which is the 30th prime, prime(30)-3*30 = 113-90 = 23 which is also prime.
|
|
MAPLE
|
KD := proc() local a, b; a:= ithprime(n); b:= abs(a-3*n); if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..500);
|
|
MATHEMATICA
|
KD = Select[Table[{Prime[n], Prime[n] - 3*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[KD][[1]]
|
|
PROG
|
|
|
CROSSREFS
|
Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A231232 (primes p : p+2*k is also prime).
Cf. A231383 (primes p : p+3*k is also prime).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|