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

1,2

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.

Example

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.

Prog

(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

Crossrefs

Cf. A219248, A281878.

Sequence in context: A277618 A358054 A219250 * A361643 A282891 A117137

Adjacent sequences: A376125 A376126 A376127 * A376129 A376130 A376131

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Sep 11 2024

Status

approved