A245650 Primes in the sequence 12*n - prime(n), (A245071).

31, 41, 59, 67, 101, 107, 139, 179, 193, 199, 211, 229, 239, 269, 271, 281, 293, 307, 313, 353, 353, 353, 379, 397, 409, 431, 439, 449, 449, 457, 467, 479, 491, 499, 509, 521, 547, 563, 599, 607, 617, 641, 659, 673, 709, 719, 739, 751, 761, 769, 809, 811, 821, 827, 859, 863, 881, 883, 911, 911, 919, 929

Offset

1,1

Comments

As the arithmetic derivative of prime numbers is [prime(n)]' = 1 the comparison of the first arithmetic derivative of (A245071)' = A245649 leads to a selection of 13.386 prime numbers out of 100.000, where some prime numbers are repeated. Remark: The sign of prime(n) here used is +, so prime(n) is distributed relative to 12 = floor(prime(n)/n).

Since 12*i - prime(i) < 0 for i > A102281(12) = 40121, this sequence is finite. It has 13386 members, with 1793 distinct primes, the largest being 16369 = a(4713). - Robert Israel, Jul 30 2014

Links

Robert Israel, Table of n, a(n) for n = 1..13386(full sequence)

Formula

a(n) is the n-th prime member of the sequence 12*i - prime(i). a(n) = prime(n) if (12*i - prime(i)) = prime(n).

Maple

A:=select(isprime, [seq(12*n - ithprime(n), n=1..40121)]); # Robert Israel, Jul 30 2014

Prog

(PARI) for(n=1, 10^3, q=12*n-prime(n); if(isprime(q), print1(q, ", "))) \\ Derek Orr, Jul 30 2014

Crossrefs

Cf. A102281, A245071, A245649.

Sequence in context: A198175 A238397 A087054 * A363187 A098711 A087053

Adjacent sequences: A245647 A245648 A245649 * A245651 A245652 A245653

Keyword

nonn,fini,full

Author

Freimut Marschner, Jul 30 2014

Status

approved