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 A376308 #8 Sep 22 2024 11:15:44 %S A376308 1,2,1,2,3,1,2,4,2,1,5,4,2,4,2,4,6,2,3,4,2,6,2,6,8,4,2,4,2,4,8,4,2,1, %T A376308 3,6,2,10,2,6,4,2,4,6,2,10,2,4,2,12,4,2,4,6,2,8,5,1,6,2,6,4,2,6,4,14, %U A376308 4,2,4,14,6,4,2,4,6,2,6,4,6,8,4,8,10,2,10 %N A376308 Run-compression of the sequence of first differences of prime-powers. %C A376308 We define the run-compression of a sequence to be the anti-run obtained by reducing each run of repeated parts to a single part. Alternatively, run-compression removes all parts equal to the part immediately to their left. For example, (1,1,2,2,1) has run-compression (1,2,1). %e A376308 The sequence of prime-powers (A246655) is: %e A376308 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, ... %e A376308 The sequence of first differences (A057820) of prime-powers is: %e A376308 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, ... %e A376308 The run-compression is A376308 (this sequence). %t A376308 First/@Split[Differences[Select[Range[100],PrimePowerQ]]] %Y A376308 For primes instead of prime-powers we have A037201, halved A373947. %Y A376308 For squarefree numbers instead of prime-powers we have A376305. %Y A376308 For run-lengths instead of compression we have A376309. %Y A376308 For run-sums instead of compression we have A376310. %Y A376308 For positions of first appearances we have A376341, sorted A376340. %Y A376308 A000040 lists the prime numbers, differences A001223. %Y A376308 A000961 and A246655 list prime-powers, differences A057820. %Y A376308 A003242 counts compressed compositions, ranks A333489. %Y A376308 A024619 and A361102 list non-prime-powers, differences A375708. %Y A376308 A116861 counts partitions by compressed sum, by compressed length A116608. %Y A376308 A373948 encodes compression using compositions in standard order. %Y A376308 Cf. A001597, A006549, A007916, A025475, A034296, A053289, A076259, A110969, A120430, A124767, A174965, A374251. %K A376308 nonn %O A376308 1,2 %A A376308 _Gus Wiseman_, Sep 20 2024