A080102 Smallest prime power in all composite numbers between n-th prime and next prime, a(n) = 1 if no such prime power exists.

4, 1, 8, 1, 16, 1, 1, 25, 1, 32, 1, 1, 1, 49, 1, 1, 64, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 121, 128, 1, 1, 1, 1, 1, 1, 1, 169, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 243, 256, 1, 1, 1, 1, 1, 1, 289, 1, 1, 1, 1, 1, 1, 343, 1, 1, 1, 361, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

2,1

Links

Amiram Eldar, Table of n, a(n) for n = 2..10000

Example

There are two prime powers between 32749 = A000040(3512) and 32771 = A000040(3513): 32761 = 181^2 and 32768 = 2^15, therefore a(3512) = 32761, A080103(3512) = 32768 and A080101(3512) = 2.

Mathematica

a[n_] := SelectFirst[Range[Prime[n] + 1, Prime[n + 1] - 1], PrimePowerQ, 1]; Array[a, 100, 2] (* Amiram Eldar, Mar 26 2025 *)

Crossrefs

Cf. A080101, A080103, A025475, A000961.

Sequence in context: A305834 A380891 A295786 * A106475 A376302 A370614

Adjacent sequences: A080099 A080100 A080101 * A080103 A080104 A080105

Keyword

nonn

Author

Reinhard Zumkeller, Jan 28 2003

Status

approved