This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385829 #27 Jul 11 2025 14:26:59 %S A385829 1,4,7,9,13,16,23,27,30,31,35,41,42,49,53,54,59,63,64,65,66,67,79,80, %T A385829 83,85,95,101,102,105,107,110,113,114,116,117,119,121,125,131,135,136, %U A385829 138,143,145,150,160,162,163,169,174,175,178,187,191,194,197,199,200,203 %N A385829 Numbers k that are the largest k such that k cannot be partitioned into parts that are a set of at least two consecutive primes. %C A385829 If we consider partitions into one distinct prime then no such largest number k exists. %H A385829 David A. Corneth, <a href="/A385829/a385829.gp.txt">Terms with their corresponding list of consecutive primes</a> %e A385829 1 is a term as it is the largest positive integer that cannot be partitioned into parts 2 and 3. We have 2 = 2, 3 = 3 and so any positive integer at least two can be partitioned into parts 2 and 3. %e A385829 30 is a term as 30 is the largest number that cannot be partitions into parts 7, 11 and 13. Proof: %e A385829 30 cannot be written as a partition of 7, 11, 13 and we have 31 = 7 + 11 + 13, 32 = 3*7 + 11, 33 = 3*11, 34 = 3*7 + 13, 35 = 5*7, 36 = 2*7 + 2*11, 37 = 11 + 2*13 which proves that the next 7 positive integers after 30 can be partitioned into parts 7, 11, 13. Any larger number than that can have more sevens added. %Y A385829 Frobenius numbers for k successive primes: A037165 (k=2), A138989 (k=3), A138990 (k=4), A138991 (k=5), A138992 (k=6), A138993 (k=7), A138994 (k=8). %K A385829 nonn %O A385829 1,2 %A A385829 _Gordon Hamilton_, Jul 09 2025 %E A385829 More terms from _David A. Corneth_, Jul 09 2025