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A377703 First differences of the sequence A345531(k) = least prime-power greater than the k-th prime.

%I A377703 #10 Nov 15 2024 09:03:52
%S A377703 1,3,1,5,3,3,4,2,6,1,9,2,4,2,10,2,3,7,2,6,2,8,8,4,2,4,2,4,8,7,9,2,10,
%T A377703 2,6,6,4,2,10,2,10,2,4,2,12,12,4,2,4,6,2,2,13,7,6,2,6,4,2,6,18,4,2,4,
%U A377703 14,6,6,6,4,6,2,12,6,4,6,8,4,8,10,2,10,2,6
%N A377703 First differences of the sequence A345531(k) = least prime-power greater than the k-th prime.
%C A377703 What is the union of this sequence? In particular, does it contain 17?
%t A377703 Differences[Table[NestWhile[#+1&, Prime[n]+1,!PrimePowerQ[#]&],{n,100}]]
%o A377703 (Python)
%o A377703 from sympy import factorint, prime, nextprime
%o A377703 def A377703(n): return -next(filter(lambda m:len(factorint(m))<=1, count((p:=prime(n))+1)))+next(filter(lambda m:len(factorint(m))<=1, count(nextprime(p)+1))) # _Chai Wah Wu_, Nov 14 2024
%Y A377703 First differences of A345531.
%Y A377703 A000961 lists the powers of primes, differences A057820.
%Y A377703 A001597 lists the perfect-powers, differences A053289, seconds A376559.
%Y A377703 A007916 lists the non-perfect-powers, differences A375706, seconds A376562.
%Y A377703 A024619 lists the non-prime-powers, differences A375735, seconds A376599.
%Y A377703 A080101 counts prime-powers between primes (exclusive).
%Y A377703 A246655 lists the prime-powers, differences A057820 without first term.
%Y A377703 A361102 lists the non-powers of primes, differences A375708.
%Y A377703 A366833 counts prime-powers between primes, see A053607, A304521, A377057 (positive), A377286 (zero), A377287 (one), A377288 (two).
%Y A377703 A377432 counts perfect-powers between primes, see A377434 (one), A377436 (zero), A377466 (multiple).
%Y A377703 Cf. A000040, A008864, A031218, A377281, A377282, A377286, A377289, A377468.
%K A377703 nonn
%O A377703 1,2
%A A377703 _Gus Wiseman_, Nov 07 2024