A376128 The absolute difference of two successive terms is prime and the absolute difference of two successive digits is also prime.

0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 13, 16, 14, 25, 20, 27, 24, 29, 42, 47, 49, 46, 35, 30, 53, 50, 31, 36, 38, 57, 52, 41, 64, 61, 63, 58, 69, 72, 70, 75, 86, 81, 68, 135, 74, 79, 242, 469, 246, 83, 85, 252, 425, 202, 413, 130, 203, 136, 131, 358, 147, 94, 92, 97, 270, 241, 302, 429, 250, 207, 205, 258, 149

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Sep 11 2024

Keywords

• base
• nonn

Examples

			Terms a(1) to a(15) are 0,2,4,1,3,5,7,9,6,8,13,16,14,25,20.
The successive absolute differences between two terms are the primes 2,2,3,2,2,2,2,3,2,5,3,2,11,5.
The successive absolute differences between two digits are the primes 2,2,3,2,2,2,2,3,2,7,2,2,5,5,3,2,3,3,2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Eric Angelini, More digits, terms and primes, personal blog of the author.

Crossrefs

Cf. A219248, A281878.

Programs

Python

# uses A219248gen in A219248
from sympy import isprime
from itertools import count, islice
def c(an, k):
    return isprime(abs(an-k)) and isprime(abs(an%10-int(str(k)[0])))
def agen(): # generator of terms
    an, aset = 0, {0}
    while True:
        yield an
        an = next(k for k in A219248gen(seed=str(an%10)) if k not in aset and c(an, k))
        aset.add(an)
print(list(islice(agen(), 73))) # Michael S. Branicky, Sep 11 2024