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A172523
Partial sums of primes in which no digit is a prime A061372.
0
89, 498, 947, 1446, 2255, 6304, 10403, 14812, 19461, 24350, 29259, 34228, 39227, 45316, 51765, 58234, 64923, 71792, 78691, 85640, 93649, 101718, 109807, 118416, 127085, 135774, 144473, 153322, 162291, 171290, 180339, 189988, 199677, 209626
OFFSET
1,1
COMMENTS
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.
FORMULA
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}.
EXAMPLE
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.
MATHEMATICA
Accumulate[Select[Prime[Range[2000]], SubsetQ[{0, 4, 6, 8, 9}, IntegerDigits[ #]]&]] (* Harvey P. Dale, Jan 21 2016 *)
CROSSREFS
Sequence in context: A051416 A279366 A142904 * A159747 A141866 A176634
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Feb 06 2010
STATUS
approved