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

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.

Links

Table of n, a(n) for n=1..34.

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

Cf. A000040, A061372.

Sequence in context: A051416 A279366 A142904 * A159747 A141866 A176634

Adjacent sequences: A172520 A172521 A172522 * A172524 A172525 A172526

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Feb 06 2010

Status

approved