A287353 -id:A287353 - cp's OEIS frontend

A379426 Prime terms in A287353.

2, 23, 2357, 23581, 2358247, 235824913, 235824916247, 2358249162515829584909, 235824916251582958491829824917162558516292249258249589629182571583855789, 2358249162515829584918298249171625585162922492582495896291825715838558298516316558918298250261

Offset: 1

Ya-Ping Lu, Dec 22 2024

nonn

Primes Sum_{i=1..k} 10^(k-i)*prime(i) for some k.

			k    prime(k)  A287353(k)  n    a(n)
---  --------  ----------  ---  -------
1    2         2           1    2
2    3         23          2    23
3    5         235
4    7         2357        3    2357
5    11        23581       4    23581
6    13        235823
7    17        2358247     5    2358247

Cf. A013918, A069151, A287353.

from sympy import isprime, nextprime
m = p = 0
while p < 500:
    p = nextprime(p); m = 10*m + p
    if isprime(m): print(m, end = ', ')

A110299 a(n) = Sum_{i=0..n-1} 2^i*prime(n-i).

Original entry on oeis.org

2, 7, 19, 45, 101, 215, 447, 913, 1849, 3727, 7485, 15007, 30055, 60153, 120353, 240759, 481577, 963215, 1926497, 3853065, 7706203, 15412485, 30825053, 61650195, 123300487, 246601075, 493202253, 986404613, 1972809335, 3945618783, 7891237693, 15782475517

Offset: 1

Ryan Propper, Sep 07 2005

Eric Angelini, "Array with primes." Pers. comm. on the SeqFan mailing list, Sep. 7 2005.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A000040, A135483, A287353.

Cf. A125180, A000720, A007504

A110299:= func< n | (&+[2^(n-j)*NthPrime(j): j in [1..n]]) >;
[A110299(n): n in [1..40]]; // G. C. Greubel, Jan 03 2023

a:= proc(n) option remember;
      `if`(n=0, 0, ithprime(n)+2*a(n-1))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Dec 10 2016

Table[Sum[2^i * Prime[n-i], {i, 0, n-1}], {n, 1, 30}]

a(n) = fromdigits(primes(n),2); \\ Kevin Ryde, Jun 22 2022

from sympy import prime
def A110299(n):
    c = 0
    for i in range(n):
        c = (c<<1)+prime(i+1)
    return c # Chai Wah Wu, Jan 04 2023

@CachedFunction # a = A110299
def a(n): return 2 if (n==1) else 2*a(n-1) + nth_prime(n)
[a(n) for n in range(1,41)] # G. C. Greubel, Jan 03 2023

G.f: b(x)/(1-2*x), where b(x) is the g.f. of A000040. - Mario C. Enriquez, Dec 10 2016
a(n) = 2*a(n-1) + A000040(n) for n>0 with a(0)=0. - Alois P. Heinz, Dec 10 2016
From Ridouane Oudra, Jan 25 2024: (Start)
a(n) = Sum_{i=0..prime(n+1)-1} (2^(n-pi(i)) - 1), where prime(n) = A000040(n) and pi(n) = A000720(n).
a(n) = A125180(n+1) - A000040(n+1);
a(n) = Sum_{i=1..n} A125180(i);
a(n) = A007504(n) + Sum_{i=1..n-1} a(i). (End)

A092844 a(n) = Sum_{k=1..n} prime(k)*10^(k-1).

Original entry on oeis.org

2, 32, 532, 7532, 117532, 1417532, 18417532, 208417532, 2508417532, 31508417532, 341508417532, 4041508417532, 45041508417532, 475041508417532, 5175041508417532, 58175041508417532, 648175041508417532

Offset: 1

Jorge Coveiro, Apr 15 2004

Robert Israel, Table of n, a(n) for n = 1..996

Cf. A038394, A135483, A287353.

ListTools:-PartialSums([seq(ithprime(i)*10^(i-1),i=1..30)]); # Robert Israel, Apr 12 2020

Array[Sum[Prime[k]*10^(k - 1), {k, #}] &, 17] (* Michael De Vlieger, Jun 22 2022 *)
Accumulate[Table[Prime[n]10^(n-1),{n,20}]] (* Harvey P. Dale, Oct 11 2022 *)

a(n) = fromdigits(Vecrev(primes(n))); \\ Kevin Ryde, Jun 22 2022

cp's OEIS Frontend

A379426 Prime terms in A287353.

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A110299 a(n) = Sum_{i=0..n-1} 2^i*prime(n-i).

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A092844 a(n) = Sum_{k=1..n} prime(k)*10^(k-1).

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