A174008 -id:A174008 - cp's OEIS frontend

A174009 Numbers n such that A174008(k)=n-th prime.

1, 4, 5, 11, 13, 16, 18, 19, 20, 25, 33, 37, 38, 39, 40, 48, 52, 59, 60, 69, 72, 73, 76, 79, 84, 85, 86, 87, 96, 98, 104, 110, 117, 122, 135, 136, 140, 142, 145, 151, 153, 160, 162, 173, 179, 183, 186, 191, 192, 199, 200, 206, 214, 218, 221, 226, 232, 234, 239, 242

Offset: 1

Juri-Stepan Gerasimov, Mar 05 2010

nonn

n-th prime in sequence A174008.

			a(1)=1 because A174008(1)=2=1st prime;
a(2)=4 because A174008(2)=7=4th prime;
a(3)=5 because A174008(3)=11=5th prime;
a(4)=11 because A174008(7)=31=11th prime.

Cf. A000040, A001477, A078916, A163300, A174008.

From R. J. Mathar, Apr 28 2010: (Start)
A163300 := proc(n) option remember ; if n = 1 then 0; else for a from procname(n-1)+2 by 2 do if not isprime(a) then return a ; end if; end do; end if; end proc:
A174008 := proc(n) ithprime(n)+A163300(n) ; end proc:
A174009 := proc(k) p := A174008(k) ; if isprime(p) then printf("%d,", numtheory[pi](p) ) ; end if; return ; end proc:
seq(A174009(k),k=1..400 ) ; (End)

More terms from R. J. Mathar, Apr 28 2010

A174010 Primes p of the form p = A000040(k) - A163300(k) for some k (includes duplicates).

Original entry on oeis.org

2, 3, 3, 5, 13, 17, 29, 31, 31, 37, 41, 47, 53, 67, 71, 71, 79, 79, 83, 89, 97, 97, 107, 107, 127, 131, 151, 181, 197, 211, 229, 241, 257, 257, 269, 271, 281, 283, 283, 311, 353, 373, 389, 401, 409, 409, 419, 419, 431, 449, 463, 479, 491, 499, 547, 563, 577, 577

Offset: 1

Juri-Stepan Gerasimov, Mar 05 2010

Primes of form k-th prime minus k-th even nonnegative nonprime.

Essentially the same as A144419.

			a(1)=2 because 2-0=2; a(2)=3 because 17-14=3; a(3)=3 because 19-16=3; a(4)=5 because 23-18=5; a(5)=13 because 37-24=13.

Cf. A144419, A001477, A078916, A163300, A174008.

A163300 := proc(n) if n <= 2 then op(n,[0,4]) ; else for a from procname(n-1)+2 by 2 do if not isprime(a) then return a; end if; end do; end if; end proc:
for n from 1 to 400 do p := ithprime(n) -A163300(n) ; if isprime(p) then printf("%d,",p) ; end if; end do: # R. J. Mathar, May 02 2010

Corrected (83 inserted) by R. J. Mathar, May 02 2010

cp's OEIS Frontend

A174009 Numbers n such that A174008(k)=n-th prime.

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