A243076 Let f(p,i) = smallest prime m >= p such that m == i (mod p); a(n) = Sum_{i=0..p-1} f(p,i), where p = n-th prime.

5, 15, 55, 119, 341, 533, 901, 1387, 1909, 3103, 4061, 5365, 6601, 7783, 9635, 12455, 16343, 17507, 20033, 24069, 27083, 29941, 33283, 42453, 47433, 53631, 54693, 60241, 66163, 69721, 86741, 92879, 104805, 102443, 126203, 130011, 136119, 143603, 157147

Offset

1,1

Comments

a(n) is always odd.

From Robert G. Wilson v, Jun 21 2017: (Start)

Obviously, prime(n)|a(n) for n>1.

a(n)/prime(n), n>1: 5, 11, 17, 31, 41, 53, 73, 83, 107, 131, 145, 161, 181, 205, 235, 277, 287, 299, 339, etc.

Values of n such that a(n) < a(n-1): 34, 51, 57, 58, 65, 69, 71, 91, 96, 105, 109, 111, ....

(End)

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Example

a(1) = 5 = 2+3,
a(2) = 15 = 3+7+5,
a(3) = 55 = 5+11+7+13+19,
a(4) = 119 = 7+29+23+17+11+19+13,
a(5) = 341 = 11+23+13+47+37+71+17+29+19+31+43, etc.

Mathematica

f[n_] := Block[{p = Prime@ n, q, i = s = 0}, While[i < p, q = If[OddQ@ i, 2, 1]*p + i; While[ !PrimeQ@ q, q += 2p]; s += q; i++]; s]; f[1] = 5; Array[f, 100] (* Robert G. Wilson v, Jun 21 2017 *)

Prog

(PARI) a(n) = {res = 0; for (index = 0, prime(n)-1, m = n; while ((prime(m) % prime(n)) != index, m++; ); res += prime(m); ); res; } \\ Michel Marcus, Jun 04 2014
(Python)
from sympy import prime, isprime
def a(n):
    if n==1: return 5
    p=prime(n)
    i=0
    s=0
    while i<p:
        q=(2 if i%2 else 1)*p + i
        while not isprime(q): q+=2*p
        s+=q
        i+=1
    return s
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 22 2017, after Mathematica code

Crossrefs

Sequence in context: A149584 A147324 A109245 * A002221 A007714 A123011

Adjacent sequences: A243073 A243074 A243075 * A243077 A243078 A243079

Keyword

nonn

Author

Torlach Rush, May 30 2014

Extensions

More terms from Michel Marcus, Jun 05 2014

Entry revised by N. J. A. Sloane, Jun 23 2017

Name corrected by Andrey Zabolotskiy, Dec 25 2023

Status

approved