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A058049
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Numbers k such that the sum of the digits of the first k primes is a prime.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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s = 0; Do[ s = s + Apply[ Plus, RealDigits[ Prime[ n ]] [[1]] ]; If[ PrimeQ[ s ], Print[ n ] ], {n, 0, 1000} ].
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PROG
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(PARI) isok(n) = isprime(sum(k=1, n, sumdigits(prime(k)))); \\ Michel Marcus, Mar 11 2017
(Python)
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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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