A053790 -id:A053790 - cp's OEIS frontend

A053789 a(n) = A020639(A053790(n)).

2, 2, 2, 7, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 41, 2, 3, 2, 3, 2, 3, 2, 3, 2, 59, 2, 7, 2, 3, 2, 3, 2, 7, 2, 37, 2, 2, 5, 2, 2, 89, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 13, 2, 109, 2, 2, 17, 2, 2, 2, 7, 2, 7, 2, 2, 7, 2

Offset: 1

Enoch Haga, Mar 27 2000

			a(4) = 7 because the sum of the first 8 primes is 77 and 7 is its least prime divisor.

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

Cf. A013918, A053790, A020639.

N:= 2000: # to use primes <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
A053790:= remove(isprime, ListTools:-PartialSums(P)):
map(t -> min(numtheory:-factorset(t)), A053790); # Robert Israel, Jan 29 2018

Edited by N. J. A. Sloane, Mar 16 2008, following explication by R. J. Mathar, Feb 26 2008

A066527 Triangular numbers that for some k are also the sum of the first k primes.

Original entry on oeis.org

10, 28, 133386, 4218060, 54047322253, 14756071005948636, 600605016143706003, 41181981873797476176, 240580227206205322973571, 1350027226921161196478736

Offset: 1

Reinhard Zumkeller, Jan 06 2002

a(n) = A000217(i) = A007504(j) for appropriate i, j.
These are the 4, 7, 516, 2904, 328777, ... -th triangular numbers and are the sums of the first 3, 5, 217, 1065, 93448, ... prime numbers respectively.
a(7) is the sum of the first 240439822 primes. a(8) is the sum of the first 1894541497 primes. - Donovan Johnson, Nov 24 2008
a(9) is the sum of the first 132563927578 primes. a(10) is the sum of the first 309101198255 primes. a(11) > 6640510710493148698166596 (sum of first pi(2*10^13) primes). - Donovan Johnson, Aug 23 2010

			a(2) = 28, as A000217(7) = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 = 2 + 3 + 5 + 7 + 11 = A007504(5).

Cf. A010054, A053790.
Intersection of A000217 and A007504.
Cf. also A061890, A364691, A366269.

a066527 n = a066527_list !! (n-1)
a066527_list = filter ((== 1) . a010054) a007504_list
-- Reinhard Zumkeller, Mar 23 2013

a066527(m) = local(d,ds,p,ps); d=1; ds=1; p=2; ps=2; while(ds

s = 0; Do[s = s + Prime[n]; t = Floor[ Sqrt[2*s]]; If[t*(t + 1) == 2s, Print[s]], {n, 1, 10^6} ]
Select[Accumulate[Prime[Range[5000000]]],IntegerQ[(Sqrt[1+8#]-1)/2]&] (* Harvey P. Dale, May 04 2013 *)

from sympy import integer_nthroot, isprime, nextprime
def istri(n): return integer_nthroot(8*n+1, 2)[1]
def afind(limit):
    s, p = 2, 2
    while s < limit:
        if istri(s): print(s, end=", ")
        p = nextprime(p)
        s += p
afind(10**11) # Michael S. Branicky, Oct 28 2021

a(5) from Klaus Brockhaus and Robert G. Wilson v, Jan 07 2002
a(6) from Philip Sung (philip_sung(AT)hotmail.com), Jan 25 2002
a(7)-a(8) from Donovan Johnson, Nov 24 2008
a(9)-a(10) from Donovan Johnson, Aug 23 2010

A338446 Numbers that are sums of consecutive odd primes.

Original entry on oeis.org

3, 5, 7, 8, 11, 12, 13, 15, 17, 18, 19, 23, 24, 26, 29, 30, 31, 36, 37, 39, 41, 42, 43, 47, 48, 49, 52, 53, 56, 59, 60, 61, 67, 68, 71, 72, 73, 75, 78, 79, 83, 84, 88, 89, 90, 95, 97, 98, 100, 101, 102, 103, 107, 109, 112, 113, 119, 120, 121, 124, 127, 128, 131, 132, 137

Offset: 1

Ilya Gutkovskiy, Oct 28 2020

nonn

			67 is in the sequence because 67 = 7 + 11 + 13 + 17 + 19.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A007504, A034707, A050936, A053790, A065091, A071148.

q:= proc(n) local p, q, s; p, q, s:= prevprime(n+1)$3;
      do if p=2 then return false
       elif s=n then return true
       elif sAlois P. Heinz, Oct 31 2020

okQ[n_] := Module[{p, q, s}, {p, q, s} = Table[NextPrime[n + 1, -1], {3}]; While[True, Which[
     p == 2, Return@ False,
     s == n, Return@ True,
     s < n, p = NextPrime[p, -1]; s = s + p,
     True, s = s - q; q = NextPrime[q, -1]]]];
Select[Range[3, 150], okQ] (* Jean-François Alcover, Feb 21 2022, after Alois P. Heinz *)

from sympy import prevprime
def ok(n):
    if n < 2: return False
    p, q, s = [prevprime(n+1)] * 3
    while True:
        if p == 2: return False
        if s == n: return True
        elif s < n: p = prevprime(p); s += p
        else: s -= q; q = prevprime(q)
print([k for k in range(150) if ok(k)]) # Michael S. Branicky, Feb 21 2022 after Alois P. Heinz

cp's OEIS Frontend

A053789 a(n) = A020639(A053790(n)).

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A066527 Triangular numbers that for some k are also the sum of the first k primes.

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A338446 Numbers that are sums of consecutive odd primes.

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Maple

Mathematica

Python