A247461 Subsequence obtained from A026242 by applying an Eratosthenes-type sieve: strike out every second number after the first "2", then if m is the next number not yet struck out, strike out every m-th number following this one, etc.

1, 1, 2, 3, 4, 5, 8, 15, 20, 35, 50, 37, 40, 46, 109, 124, 134, 92, 183, 198, 223, 159, 272, 282, 205, 214, 356, 371, 406, 445, 480, 495, 312, 321, 569, 579, 367, 628, 653, 434, 742, 801, 816, 851, 535, 925, 940, 587, 596, 999, 1014, 1024, 709, 755, 1261

Offset

1,3

Comments

The first two terms a(1)=a(2)=1 are included here but are not considered to be part of what one might call A026242-primes, in analogy of the usual primes A000040 obtained by applying the very same procedure to the set of all positive integers.

Since A026242 is not increasing, this sequence isn't, either. However, since the remaining "primes" > 1 are exactly the numbers used during the sieve, and for all m, the second m occurs m places after the first m in A026242, no number can occur twice here.

There is a stronger version of the sieve, which consists of considering all numbers "m", whether or not they have been crossed out earlier. When this is applied, then the result is the finite subsequence [1, 1, 2, 3, 4, 5, 8, 15, 50]. Eric Angelini calls these numbers, {2, 3, 4, 5, 8, 15, 50}, "Biprimes of K = A026242".

Links

Table of n, a(n) for n=1..55.

E. Angelini, Biprimes of K, Sep 17 2014

Prog

(PARI) /* first compute A026242 to a sufficient number of terms, then: */ for(k=3, #K=A026242, K[k] && forstep(i=k+K[k], #K, K[k], K[i]=0)); A247461=select(x->x, K)
/* to apply the stronger sieve */ for(k=3, #K=A026242, forstep(i=k+A026242[k], #K, A026242[k], K[i]=0)); select(x->x, K)

Crossrefs

Sequence in context: A075721 A112479 A333264 * A281303 A264011 A337280

Adjacent sequences: A247458 A247459 A247460 * A247462 A247463 A247464

Keyword

nonn

Author

M. F. Hasler and Eric Angelini, Sep 17 2014

Status

approved