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A219248
Numbers such that the absolute difference of any two adjacent (decimal) digits is prime.
8
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Apr 12 2013
STATUS
approved