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A058049 Numbers n such that the sum of the digits of the n first primes is a prime. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..59.

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

EXAMPLE

5 is a term because sum of digits of 5 first 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.

MATHEMATICA

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

PROG

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

CROSSREFS

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

Cf. A051351.

Sequence in context: A101742 A194831 A111688 * A091871 A303393 A039085

Adjacent sequences:  A058046 A058047 A058048 * A058050 A058051 A058052

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Nov 18 2000

EXTENSIONS

Edited by R. J. Mathar, Aug 04 2008

STATUS

approved

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Last modified January 18 21:54 EST 2019. Contains 319282 sequences. (Running on oeis4.)