A036439 -id:A036439 - cp's OEIS frontend

A014284 Partial sums of primes, if 1 is regarded as a prime (as it was until quite recently, see A008578).

1, 3, 6, 11, 18, 29, 42, 59, 78, 101, 130, 161, 198, 239, 282, 329, 382, 441, 502, 569, 640, 713, 792, 875, 964, 1061, 1162, 1265, 1372, 1481, 1594, 1721, 1852, 1989, 2128, 2277, 2428, 2585, 2748, 2915, 3088, 3267, 3448, 3639, 3832, 4029

Offset: 1

Deepan Majmudar (dmajmuda(AT)esq.com)

Lexicographically earliest sequence whose first differences are an increasing sequence of primes. Complement of A175969. - Jaroslav Krizek, Oct 31 2010
A175944(a(n)) = A018252(n). - Reinhard Zumkeller, Mar 18 2011
Partial sums of noncomposite numbers (A008578). - Omar E. Pol, Aug 09 2012

			a(7) = 42 because the first six primes (2, 3, 5, 7, 11, 13) add up to 41, and 1 + 41 = 42.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A007504.
Equals A036439(n) - 1.
Cf. A175965, A175966, A175967, A175968, A175969, A051349, A175970. - Jaroslav Krizek, Oct 31 2010
Cf. A008578.

a014284 n = a014284_list !! n
a014284_list = scanl1 (+) a008578_list
-- Reinhard Zumkeller, Mar 26 2015

[1] cat [1 + (&+[NthPrime(j): j in [1..n]]): n in [1..50]]; // G. C. Greubel, Jun 18 2019

A014284 := proc(n)
    add(A008578(i),i=1..n) ;
end proc:
seq(A014284(n),n=1..60) ; # R. J. Mathar, Mar 05 2017

Join[{1}, Table[1+Sum[Prime[j], {j,1,n}], {n,1,50}]] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2009, modified by G. C. Greubel, Jun 18 2019 *)
Accumulate[Join[{1}, Prime[Range[45]]]] (* Alonso del Arte, Oct 09 2012 *)

concat([1], vector(50, n, 1 + sum(j=1,n, prime(j)) )) \\ G. C. Greubel, Jun 18 2019

[1]+[1 + sum(nth_prime(j) for j in (1..n)) for n in (1..50)] # G. C. Greubel, Jun 18 2019

a(n) = Sum_{k <= n} [(A158611(k + 1)) * (A000012(n - k + 1))] = Sum_{k <= n} [(A158611(k + 1)) * (A000012(k))] = Sum_{k <= n} [(A008578(k)) * (A000012(n - k + 1))] = Sum_{k <= n} [(A008578(k)) * (A000012(k))] for n, k >= 1. - Jaroslav Krizek, Aug 05 2009
a(n + 1) = A007504(n) + 1. a(n + 1) - a(n) = A000040(n) = n-th primes. - Jaroslav Krizek, Aug 19 2009
a(n) = a(n-1) + prime(n-1), with a(1)=1. - Vincenzo Librandi, Jul 27 2013
G.f: (x*(1+b(x)))/(1-x) = c(x)/(1-x), where b(x) and c(x) are respectively the g.f. of A000040 and A008578. - Mario C. Enriquez, Dec 10 2016

Correction for Aug 2009 change of offset in A158611 and A008578 by Jaroslav Krizek, Jan 27 2010

A175965 Lexicographically earliest sequence with first differences as increasing sequence of noncomposites A008578.

Original entry on oeis.org

1, 2, 4, 7, 12, 19, 30, 43, 60, 79, 102, 131, 162, 199, 240, 283, 330, 383, 442, 503, 570, 641, 714, 793, 876, 965, 1062, 1163, 1266, 1373, 1482, 1595, 1722, 1853, 1990, 2129, 2278, 2429, 2586, 2749, 2916, 3089, 3268, 3449, 3640, 3833, 4030, 4229, 4440, 4663

Offset: 1

Jaroslav Krizek, Oct 31 2010

nonn

Complement of A175966.

A175944(a(n)) = A018252(n). - Reinhard Zumkeller, Mar 18 2011

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A008578, A014284, A018252, A036439, A051349.

Cf. A175944, A175966, A175967, A175968, A175969, A175970.

a175965 n = a175965_list !! n
a175965_list = scanl (+) 1 a008578_list
-- Reinhard Zumkeller, Mar 26 2015

FoldList[Plus,1,Join[{1},Prime[Range[50]]]] (* or *) Accumulate[ Join[ {1,1},Prime[Range[50]]]] (* Harvey P. Dale, Sep 28 2016 *)

a(n) = A036439(n-1) for n > 1.
a(n) - a(n-1) = A008578(n-1) for n > 1.
a(n) = A014284(n-1) + 1 for n > 1.

A227547 a(n) = a(n-1) + prime(n-1), with a(1)=3.

Original entry on oeis.org

3, 5, 8, 13, 20, 31, 44, 61, 80, 103, 132, 163, 200, 241, 284, 331, 384, 443, 504, 571, 642, 715, 794, 877, 966, 1063, 1164, 1267, 1374, 1483, 1596, 1723, 1854, 1991, 2130, 2279, 2430, 2587, 2750, 2917, 3090, 3269, 3450, 3641, 3834, 4031, 4230, 4441, 4664

Offset: 1

Vincenzo Librandi, Jul 27 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A007504, A014284, A036439.

[IsOne(n) select 3 else Self(n-1)+NthPrime(n-1): n in [1..50]]; // Bruno Berselli, Jul 30 2013

Mathematica
```
Accumulate[Join[{3}, Prime[Range[60]]]]
```

a(n) = A036439(n) + 1 = A014284(n) + 2 = A007504(n-1) + 3 (in this case, n>1).

A262392 a(n) = A007504(n) + A010693(n).

Original entry on oeis.org

2, 5, 7, 13, 19, 31, 43, 61, 79, 103, 131, 163, 199, 241, 283, 331, 383, 443, 503, 571, 641, 715, 793, 877, 965, 1063, 1163, 1267, 1373, 1483, 1595, 1723, 1853, 1991, 2129, 2279, 2429, 2587, 2749, 2917, 3089, 3269, 3449, 3641, 3833, 4031, 4229

Offset: 0

Altug Alkan, Sep 21 2015

Sequence is interesting because of the fact that a(n) is a prime number for n = 0..20.

Main inspiration of sequence was indices of prime numbers in A036439 and A227547.

			a(0) = A007504(0) + A010693(0) = 0 + 2 = 2.
a(1) = A007504(1) + A010693(1) = 2 + 3 = 5.
a(2) = A007504(2) + A010693(2) = 5 + 2 = 7.
a(3) = A007504(3) + A010693(3) = 10 + 3 = 13.
a(4) = A007504(4) + A010693(4) = 17 + 2 = 19.
a(5) = A007504(5) + A010693(5) = 28 + 3 = 31.

Cf. A036439, A227547, A007504, A010693, A071148.

s = Accumulate@ Prime@ Range@ 1200; {2}~Join~Table[s[[n]] + If[OddQ@ n, 3, 2], {n, 46}] (* Michael De Vlieger, Sep 21 2015 *)

a(n) = sum(k=1, n, prime(k)) + (n%2) + 2;
vector(50, n, a(n-1))

a(n) = Sum_{k=1..n} prime(k) + n mod 2 + 2 for n>0, a(0)=2 (from Pari code).

cp's OEIS Frontend

A014284 Partial sums of primes, if 1 is regarded as a prime (as it was until quite recently, see A008578).

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A175965 Lexicographically earliest sequence with first differences as increasing sequence of noncomposites A008578.

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A227547 a(n) = a(n-1) + prime(n-1), with a(1)=3.

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Magma

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A262392 a(n) = A007504(n) + A010693(n).

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