A219248 Numbers such that the absolute difference of any two adjacent (decimal) digits is prime.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 18, 20, 24, 25, 27, 29, 30, 31, 35, 36, 38, 41, 42, 46, 47, 49, 50, 52, 53, 57, 58, 61, 63, 64, 68, 69, 70, 72, 74, 75, 79, 81, 83, 85, 86, 92, 94, 96, 97, 130, 131, 135, 136, 138, 141, 142, 146, 147, 149, 161, 163, 164

Offset: 1

Author

M. F. Hasler, Apr 12 2013

Keywords

• nonn
• base

Comments

Numbers which may (and do) occur in A219250 and A219249 (union {0}).

This is to A219250 and A219249 what A182175 is to A182177 and A182178.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
• E. Angelini, Any digit-pair in S sums to a prime, SeqFan list, Apr 11 2013

Programs

Mathematica

Select[Range[0,200],And@@PrimeQ[Abs[Differences[IntegerDigits[#]]]]&] (* Harvey P. Dale, Jun 06 2014 *)

PARI

is_A219248(n)={!for(i=2,#n=digits(n),isprime(abs(n[i-1]-n[i]))||return)}

Python

def ok(n):
    d = list(map(int, str(n)))
    return all(abs(d[i]-d[i-1]) in {2,3,5,7} for i in range(1, len(d)))
print([k for k in range(164) if ok(k)]) # Michael S. Branicky, Sep 11 2024

Python

from itertools import count, islice
def A219248gen(seed=None): # generator of terms
    nxt = {None:"123456789", "0":"2357", "1":"3468", "2":"04579",
        "3":"01568", "4":"12679", "5":"02378", "6":"13489",
        "7":"02459", "8":"1356", "9":"2467"}
    def bgen(d, seed=None):
        if d == 0: yield tuple(); return
        yield from ((i,)+t for i in nxt[seed] for t in bgen(d-1, seed=i))
    yield 0
    for d in count(1):
        yield from (int("".join(t)) for t in bgen(d, seed=seed))
print(list(islice(A219248gen(), 65))) # Michael S. Branicky, Sep 11 2024