A397789

a(n) = nearest prime to prime(n)^(3/2).

Created: 7/24/2026 | Author: James C. McMahon and Vincenzo Manto , Jul 09 2026

This sequence has been cited by and influenced 2 other sequences

Official Comments

There is no solution for p^3 = q^2 when p and q are distinct prime numbers.

Sequence Chart

Data

3,5,11,19,37,47,71,83,109,157,173,227,263,281,317,383,457,479,547,599,619,701,757,839,953,1013,1049,1109,1129,1201,1433,1499,1601,1637,1823,1861,1973,2081,2161,2273,2393,2437,2633,2683,2767,2803,3067,3331,3413

Formula

Conjecture: A397790(n) = a(n)^2. [In other words, it is conjectured that there are no consecutive primes p1 < p2 and a prime q such that (p1 + p2)^2/4 < q^3 < (p1^2 + p2^2)/2. - _Jianing Song_, Jul 14 2026]

Computational Implementations

PARI

a(n) = my(t=prime(n)^(3/2), mn=precprime(t), mx=nextprime(t)); if(mx-t<t-mn, mx, mn); \\ _Michel Marcus_, Jul 13 2026

Mathematica

a[n_]:=Sqrt[Nearest[{NextPrime[Prime[n]^1.5,-1]^2,NextPrime[Prime[n]^1.5]^2},Prime[n]^3][[1]]];Array[a,49]

Cross-References

See also OEIS entries: Cf A000040 A001248 A002821 A030078 A077118 A397790