A104247 -id:A104247 - cp's OEIS frontend

A058049 Numbers k such that the sum of the digits of the first k primes is a prime.

1, 2, 4, 5, 6, 7, 8, 11, 12, 14, 23, 33, 43, 45, 48, 64, 69, 72, 73, 77, 87, 94, 95, 96, 98, 110, 118, 124, 130, 133, 140, 148, 152, 154, 157, 162, 171, 174, 178, 181, 196, 200, 201, 206, 210, 212, 219, 232, 241, 244, 253, 257, 267, 269, 272, 277, 299, 304, 306

Offset: 1

Robert G. Wilson v, Nov 18 2000

What is intriguing about this sequence is that the number of primes less than 10^m is of the same magnitude as A006880. Here they begin 7, 25, 122, 934.

			5 is a term because sum of digits of first 5 primes, 2+3+5+7+(1+1)=19, is prime.
a(5) = 6 because in A051351(6) = 2 + 3 + 5 + 7 + 2 (sum of eleven's digits) + 4 (sum of thirteen's digits) which equals the sum of the digits through the sixth prime = 23 which itself is a prime.

Z. Stankova-Frenkel and J. West, Explicit enumeration of 321,hexagon-avoiding permutations, arXiv:math/0106073 [math.CO], 2001.

Corresponding primes: A104247. Primes: A000040, sum of digits of primes: A007605.

Cf. A051351.

s = 0; Do[ s = s + Apply[ Plus, RealDigits[ Prime[ n ]] [[1]] ]; If[ PrimeQ[ s ], Print[ n ] ], {n, 1, 1000} ]

isok(n) = isprime(sum(k=1, n, sumdigits(prime(k)))); \\ Michel Marcus, Mar 11 2017

from sympy import isprime, nextprime
def sd(n): return sum(map(int, str(n)))
def aupto(limit):
    alst, k, p, s = [], 1, 2, 2
    while k <= limit:
        if isprime(s): alst.append(k)
        k += 1; p = nextprime(p); s += sd(p)
    return alst
print(aupto(306)) # Michael S. Branicky, Jul 18 2021

Edited by R. J. Mathar, Aug 04 2008

A075544 Primes which are the sum of the digital root of the first n primes for some n.

Original entry on oeis.org

2, 5, 17, 19, 23, 31, 37, 43, 71, 163, 179, 199, 263, 269, 347, 379, 389, 443, 467, 487, 499, 569, 601, 641, 643, 647, 683, 691, 709, 769, 821, 829, 857, 859, 919, 941, 947, 953, 967, 997, 1019, 1021, 1061, 1093, 1123, 1153, 1231, 1249, 1381, 1409, 1459

Offset: 1

Jon Perry, Oct 11 2002

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A010888, A104247.

s = 0; Do[s = s + Mod[ Prime[n], 9]; If[ PrimeQ[s], Print[s]], {n, 1, 350} ]
Select[Accumulate[Mod[Prime[Range[1000]],9]],PrimeQ] (* Harvey P. Dale, May 04 2012 *)

sumdigits2(n)=local(c); while (n>9,c=0; while (n>0,c=c+n%10; n=n-n%10; n=n/10); n=c); n
c=0; forprime (p=2,1000,c=c+sumdigits2(p); if (isprime(c),print1(c,",")))

Edited by Robert G. Wilson v, Oct 14 2002
Definition corrected by M. F. Hasler, Apr 04 2007
Corrected by Harvey P. Dale, May 04 2012

cp's OEIS Frontend

A058049 Numbers k such that the sum of the digits of the first k primes is a prime.

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