A038361 -id:A038361 - cp's OEIS frontend

A172188 Partial sums of primes of the form 3*k-1.

2, 7, 18, 35, 58, 87, 128, 175, 228, 287, 358, 441, 530, 631, 738, 851, 982, 1119, 1268, 1435, 1608, 1787, 1978, 2175, 2402, 2635, 2874, 3125, 3382, 3645, 3914, 4195, 4488, 4799, 5116, 5463, 5816, 6175, 6558, 6947, 7348, 7767, 8198, 8641, 9090, 9551, 10018

Offset: 1

Juri-Stepan Gerasimov, Jan 29 2010, Feb 01 2010

nonn

			a(1)=3*1-1=2, a(2)=2+3*2-1=7.

Cf. A038361.

Contribution from R. J. Mathar, Apr 24 2010: (Start)
A003627 := proc(n) if n <= 2 then op(n,[2,5]) ; else for a from procname(n-1)+2 by 2 do if isprime(a) and (a mod 3) =2 then return a ; end if; end do: end if; end proc:
A172188 := proc(n) add( A003627(i),i=1..n) ; end proc: seq(A172188(n),n=1..80) ; (End)

Accumulate[Select[Prime[Range[100]],IntegerQ[(#+1)/3]&]]  (* Harvey P. Dale, Apr 04 2011 *)

Entries checked by R. J. Mathar, Apr 24 2010

A354573 Prime partial sums of the primes == 5 (mod 6).

Original entry on oeis.org

5, 173, 439, 1117, 1433, 2633, 3643, 6173, 11489, 22727, 25867, 36523, 51341, 71707, 80347, 89413, 98947, 102203, 119869, 135209, 155653, 173087, 182233, 196387, 226063, 298031, 353921, 367219, 460127, 483179, 498859, 547387, 555683, 572581, 826201, 932801, 988453, 1057741, 1203421, 1253999

Offset: 1

J. M. Bergot and Robert Israel, Aug 18 2022

nonn

Primes in A038361.

			a(2) = 173 is a term because 173 = A038361(7) = 5+11+17+23+29+41+47 and is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A038361, A354572.

R:= NULL: count:= 0: t:= 0:
for p from 5 by 6 while count < 100 do
  if isprime(p) then
    t:= t+p;
    if isprime(t) then R:= R, t; count:= count+1 fi
  fi
od:
R;

Select[Accumulate[Select[Prime[Range[1000]], Mod[#, 6] == 5 &]], PrimeQ] (* Amiram Eldar, Aug 19 2022 *)

cp's OEIS Frontend

A172188 Partial sums of primes of the form 3*k-1.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

Extensions