..
NOM :
Number of polyhedral components after the n-th stage of the fractal decomposition of the Stella octangula, where only regular (equilateral) tetrahedra are subdivided.
DONNÉES :
2, 3, 5, 7, 131, 311, 887, 1013, 1949, 2399, 2621, 2957, 3251, 3323, 3701, 4289, 4919, 4973, 5099, 5101, 5477, 5927, 5981, 6359, 6599, 6779, 6863, 8069, 8447, 8573, 8627, 8669, 8951, 9677, 10141, 10181, 10211, 10589, 10631, 11399, 11597, 12101, 12479, 12659, 12983
OFFSET (décalage) :
1
COMMENTAIRES :
A prime p belongs to this sequence if in both bases 8 and 10 the iterative digit-sum process yields only prime values down to one of {2, 3, 5, 7}.
RÉFÉRENCES :
..
LIENS :
https://www.lascoux.com/wp-content/uploads/2025/12/A384306-Recursive-Digit-Sum-Stable-Primes-in-Base-8-and-Base-10.pdf
https://www.lascoux.com/wp-content/uploads/2025/12/A384306-bfile_TAG_recursive.txt
FORMULE :
..
EXEMPLE :
a(5) = 131:
In base 8: 131 = 203_8 -> 2+0+3 = 5 -> 5 is prime -> ends in 5.
In base 10: 1+3+1 = 5 -> 5 is prime -> ends in 5.
All intermediate values for both bases are primes, and the last values are in {2,3,5,7}.
a(6) = 887:
In base 8: 887 = 1567_8 -> 1+5+6+7 = 19 -> 19 is prime -> 19 = 23_8 -> 2+3 = 5-> 5 is prime -> ends in 5.
In base 10: 8+8+7 = 23 -> 23 is prime -> 2+3 = 5 -> 5 is prime -> ends in 5.
All intermediate values for both bases are primes, and the last values are in {2,3,5,7}.
PROGRAMME (autre langage) :
Python)
from gmpy2 import is_prime, digits
f = lambda n, b: True if n < b else (f(s, b) if is_prime(s:=sum(map(int, digits(n, b)))) else False)
print([p for p in range(2, 13001) if is_prime(p) and f(p, 10) and f(p, 8)])
RÉFÉRENCES CROISÉES :
Subsequence of A070027.
Cf. A000040, A007953.
Sequence in context: A071119 A157869 A046705 * A054218 A075048 A281021
Adjacent sequences: A384303 A384304 A384305 * A384307 A384308 A384309
MOTS-CLÉS :
nonn,easy
AUTEUR :
Jean-Louis Lascoux — 2025-12-05
