A383318 Lexicographically earliest sequence of distinct terms such that replacing each term k with prime(k) does not change the succession of digits.

6455, 3, 5, 1, 12, 37, 15, 7, 4, 71, 77, 35, 33, 8, 9, 14, 91, 371, 92, 34, 346, 72, 53, 94, 79, 13, 923, 39, 359, 2, 41, 49, 140, 141, 721, 916, 724, 17, 31, 792, 27, 80, 98, 11, 54, 497, 159, 547, 95, 912, 760, 73, 10, 340, 952, 131, 25, 135, 47, 93, 739, 43

Offset: 1

Author

Dominic McCarty, Apr 23 2025

Keywords

• nonn
• base

Examples

			Let b(n) = prime(a(n))
(a(n)): 6455, 3, 5, 1, 12, 37, 15, 7, 4, 71, 77, ...
(b(n)): 64553,   5, 11, 2, 37, 157,   47, 17, 7, ...
		

Links

• Dominic McCarty, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A383319 (prime(a(n))), A067928, A383320, A383322, A302656.

Programs

Python

from sympy import prime
from itertools import count
a, sa, sb = [6455], "6455", "64553"
for _ in range(30):
    a.append(next(n for k in count(1) if not (n := int(sb[len(sa):len(sa)+k])) in a and not (len(sb) > len(sa) + k and sb[len(sa) + k] == "0")))
    sa += str(a[-1]); sb += str(prime(a[-1]))
print(a)