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 A379542 #12 Jan 12 2025 23:55:18
%S A379542 3,2,0,2,-6,14,-30,62,-122,220,-344,412,-176,-944,4112,-11414,26254,
%T A379542 -53724,100710,-175034,281660,-410896,506846,-391550,-401486,2962260,
%U A379542 -9621128,24977308,-57407998,120867310,-236098336,428880422,-719991244,1096219280
%N A379542 Second term of the n-th differences of the prime numbers.
%C A379542 Also the inverse zero-based binomial transform of the odd prime numbers.
%F A379542 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * prime(k+2).
%t A379542 nn=40;Table[Differences[Prime[Range[nn+2]],n][[2]],{n,0,nn}]
%o A379542 (PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(n,k) * prime(k+2)); \\ _Michel Marcus_, Jan 12 2025
%Y A379542 For all primes (not just odd) we have A007442.
%Y A379542 Including 1 in the primes gives A030016.
%Y A379542 Column n=2 of A095195.
%Y A379542 The version for partitions is A320590 (first column A281425), see A175804, A053445.
%Y A379542 For nonprime instead of prime we have A377036, see A377034-A377037.
%Y A379542 Arrays of differences: A095195, A376682, A377033, A377038, A377046, A377051.
%Y A379542 A000040 lists the primes, differences A001223, A036263.
%Y A379542 A002808 lists the composite numbers, differences A073783, A073445.
%Y A379542 A008578 lists the noncomposite numbers, differences A075526.
%Y A379542 Cf. A064113, A065890, A084758, A140119, A173390, A258025, A258026, A293467, A333214, A333254, A377041.
%K A379542 sign
%O A379542 0,1
%A A379542 _Gus Wiseman_, Jan 12 2025