A377294 a(n) is the least n-digit prime which is the sum of the squares of three consecutive numbers, or -1 if no such prime exists.

5, 29, 149, 1877, 11909, 100469, 1026677, 10013789, 100676549, 1000611509, 10007613149, 100003082789, 1000092600389, 10000275414869, 100000426365677, 1000004865589109, 10000013191662677, 100000034139489269, 1000000221045632669, 10000000313838962309, 100000002116695737029

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Example

29 is the smallest 2-digit prime number that can be expressed as the sum of the squares of three consecutive numbers. Specifically, the sum of the squares of the numbers from 2 to 4 is 29: Sum_{i=1..3} (1+i)^2 = 2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29.

Prog

(Python)
from math import isqrt
from sympy import isprime
from itertools import count
def f(m): return sum((m+i)**2 for i in range(3))
def a(n):
    b = 10**(n-1)
    m = isqrt(b//3) - 2
    m += m&1  # note: m must be even for f(m) to be odd
    return next(t for i in count(m, 2) if (t:=f(i)) >= b and isprime(t))
print([a(n) for n in range(2, 22)]) # Michael S. Branicky, Oct 25 2024

Crossrefs

Primes in A120328.

Cf. A376992.

Sequence in context: A065541 A060926 A320089 * A239715 A260752 A098780

Adjacent sequences: A377291 A377292 A377293 * A377295 A377296 A377297

Keyword

nonn,base

Author

Jean-Marc Rebert, Oct 23 2024

Status

approved