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

1,3

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A052061 A045540 A119509 * A055568 A360822 A283161

Adjacent sequences: A219245 A219246 A219247 * A219249 A219250 A219251

Keyword

nonn,base

Author

M. F. Hasler, Apr 12 2013

Status

approved