%I #3 Apr 03 2023 10:36:11
%S 1,3,16,53,160,273,410,1423,2460,3539,4776,6143,7522,17601,27724,
%T 37860,47999,58236,68515,78882,89261,101640,115319,215598,315977,
%U 417214,519561,621940,725619,849098,1850335,2852682,3855061,4858740,5871089
%N Partial sums of A072857.
%C 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?
%H Chris K. Caldwell AND G. L. Honaker, Jr., <a href="https://t5k.org/curios/includes/glossary.pdf">A BRIEF PRIME CURIOS! GLOSSARY</a>.
%F 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}.
%e 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.
%Y Cf. A000040, A072857, A039993, A075053, A076497, A076449, A119535 (prime subsequence).
%K base,easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Feb 08 2010