A173052 Partial sums of A072857.

1, 3, 16, 53, 160, 273, 410, 1423, 2460, 3539, 4776, 6143, 7522, 17601, 27724, 37860, 47999, 58236, 68515, 78882, 89261, 101640, 115319, 215598, 315977, 417214, 519561, 621940, 725619, 849098, 1850335, 2852682, 3855061, 4858740, 5871089

Offset: 1

Author

Jonathan Vos Post, Feb 08 2010

Keywords

• base
• easy
• nonn

Comments

Partial sums of primeval numbers. Primeval number: a prime which "contains" more primes in it than any preceding number. Here "contains" means may be constructed from a subset of its digits. E.g., 1379 contains 3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97, 137, 139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971, 1973, 3719, 3917, 7193, 9137, 9173 and 9371. The subsequence of prime partial sums of primeval numbers begins: 3, 53, 1423, 3539, 6143, 89261, 115319, 315977. What is the smallest primeval prime partial sums of primeval numbers, i.e. the intersection of this sequence with A119535?

Examples

			a(36) = 1 + 2 + 13 + 37 + 107 + 113 + 137 + 1013 + 1037 + 1079 + 1237 + 1367 + 1379 + 10079 + 10123 + 10136 + 10139 + 10237 + 10279 + 10367 + 10379 + 12379 + 13679 + 100279 + 100379 + 101237 + 102347 + 102379 + 103679 + 123479 + 1001237 + 1002347 + 1002379 + 1003679 + 1012349 + 1012379.
		

Links

• Chris K. Caldwell AND G. L. Honaker, Jr., A BRIEF PRIME CURIOS! GLOSSARY.

Crossrefs

Cf. A000040, A072857, A039993, A075053, A076497, A076449, A119535 (prime subsequence).

Formula

a(n) = SUM[i=1..n] A072857(i) = SUM[i=1..n] {numbers that set a record for the number of distinct primes that can be obtained by permuting some subset of their digits}.