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A172523 Partial sums of primes in which no digit is a prime A061372. 0

%I

%S 89,498,947,1446,2255,6304,10403,14812,19461,24350,29259,34228,39227,

%T 45316,51765,58234,64923,71792,78691,85640,93649,101718,109807,118416,

%U 127085,135774,144473,153322,162291,171290,180339,189988,199677,209626

%N Partial sums of primes in which no digit is a prime A061372.

%C The "Prime Curios" web site calls the underlying sequence "holey primes... primes that have only digits with holes, i.e., 0, 4, 6, 8, or 9." The subsequence of prime partial sums begins: 89, 39227, 78691, 109807, 330233.

%F a(n) = SUM[i=1..n] A061372(i) = SUM[i=1..n] {Primes in which no digit is a prime} = SUM[i=1..n] {primes having only 0,4,6,8,9 as digits}.

%e a(3) = 89 + 409 + 449 = 947 is prime. a(13) = 89 + 409 + 449 + 499 + 809 + 4049 + 4099 + 4409 + 4649 + 4889 + 4909 + 4969 + 4999 = 39227 is prime. a(19) = 89 + 409 + 449 + 499 + 809 + 4049 + 4099 + 4409 + 4649 + 4889 + 4909 + 4969 + 4999 + 6089 + 6449 + 6469 + 6689 + 6869 + 6899 = 78691 is prime. a(23) = 89 + 409 + 449 + 499 + 809 + 4049 + 4099 + 4409 + 4649 + 4889 + 4909 + 4969 + 4999 + 6089 + 6449 + 6469 + 6689 + 6869 + 6899 + 6949 + 8009 + 8069 + 8089 = 109807 is prime. a(37) = 89 + 409 + 449 + 499 + 809 + 4049 + 4099 + 4409 + 4649 + 4889 + 4909 + 4969 + 4999 + 6089 + 6449 + 6469 + 6689 + 6869 + 6899 + 6949 + 8009 + 8069 + 8089 + 8609 + 8669 + 8689 + 8699 + 8849 + 8969 + 8999 + 9049 + 9649 + 9689 + 9949 + 40009 + 40099 + 40499 = 330233 is prime.

%t Accumulate[Select[Prime[Range[2000]],SubsetQ[{0,4,6,8,9}, IntegerDigits[ #]]&]] (* _Harvey P. Dale_, Jan 21 2016 *)

%Y Cf. A000040, A061372.

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 06 2010

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Last modified June 20 21:11 EDT 2021. Contains 345245 sequences. (Running on oeis4.)