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 A344989 #30 Aug 26 2025 00:38:18 %S A344989 2,16,26,33,55,59,0,0,124,159,233,227,276,0,372,480,0,0,0,752,0,920,0, %T A344989 1011,0,1211,1425,0,0,0,0,0,2050,2336,2495,0,0,0,0,3340,0,3712,0,0, %U A344989 4303,0,0,0,0,5195,0,5669,0,6163,6673,0,0,0,7504,0,0,8670,0,9304,9623,0,0,0,10638,10981,0,12062,0 %N A344989 Smallest number whose number of partitions into n distinct primes is n, or zero if there are no such partitions. %C A344989 From _David A. Corneth_, Aug 21 2025: (Start) %C A344989 How to prove a 0? I used the heuristic: %C A344989 a(n) = 0 if 2*n consecutive integers can be written in strictly more than n ways as a sum of n distinct primes and up to that point no positive integer has exactly n such ways. %C A344989 What other rules where used? (End) %H A344989 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/cpage/41746.html">Prime Curios! 233</a> %e A344989 a(2) = 16 because 16 is the smallest number whose number of partitions into 2 distinct primes is 2; 16 = 3+13 = 5+11. %Y A344989 Cf. A364692 asks for the largest number with the same properties. %Y A344989 Cf. A000586, A077914, A117929, A125688, A219180, A219198, A219199, A219200, A219201, A219202, A219203, A219204. %K A344989 nonn,more,changed %O A344989 1,1 %A A344989 _Metin Sariyar_, Jun 04 2021 %E A344989 a(12)-a(20) from _Alois P. Heinz_, Jun 04 2021 %E A344989 More terms from _David A. Corneth_, Aug 21 2025