A378671 a(n) is the number of cases in which prime(n) is either one of the three primes in the p, p + k and p + 2k arithmetic progressions in A120627.

0, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 4, 2, 3, 4, 3, 2, 2, 3, 5, 2, 3, 4, 3, 2, 3, 1, 3, 3, 2, 4, 2, 4, 3, 2, 2, 3, 3, 3, 6, 3, 3, 4, 3, 2, 2, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 2, 2, 3, 4, 4, 3, 4, 4, 3, 2, 3, 2, 4, 2, 3, 2, 2, 4, 3, 4, 2, 2, 2, 2, 2, 4, 4, 2, 3, 3, 3, 2

Offset

1,3

Links

Table of n, a(n) for n=1..106.

Example

a(16) = 4 because prime(16) = 53 is involved in exactly four cases in A120627:
  firstly, as prime(10) + 2k = 29 + 2*12 = 53, where k = A120627(10) = 12;
  secondly, as prime(13) + 2k = 41 + 2*6 = 53, where k = A120627(13) = 6;
  thirdly, as prime(15) + k = 47 + 6 = 53, where k = A120627(15) = 6;
  and fourthly, as prime(16) = 53 itself, in front of a progression with k = A120627(16) = 18.
Visualization of the ranges of the four progressions:
          29  31  37  41  43  47  53  59  61  67  71  73  79  83  89
 k = 12    |___________|___________|
 k =  6                |_______|___|
 k =  6                        |___|___|
 k = 18                            |_______________|_______________|
                                   ^
                                   |
                             prime(16) = 53
                              in a(16) = 4
                              progressions
                               in A120627

Prog

(PARI)
a(max_n) = { my(mp=prime(max_n), v=vector(mp), vv=vector(max_n)); for(n=0, max_n, if(n<2, 0, my(p=prime(n), k); while(!isprime(p+k++)||!isprime(p+2*k), ); if(p+k<=mp, v[p+k]++); if(p<=mp, v[p]++); if(p+2*k<=mp, v[p+2*k]++))); for(n=1, max_n, vv[n]=v[prime(n)]); vv } \\ Thomas Scheuerle, Dec 05 2024

Crossrefs

Cf. A000040, A120627.

Sequence in context: A236531 A332334 A217403 * A081309 A329377 A380783

Adjacent sequences: A378668 A378669 A378670 * A378672 A378673 A378674

Keyword

nonn

Author

Tamas Sandor Nagy, Dec 03 2024

Status

approved