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URL: https://oeis.org/A375614

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A375614
Lexicographically earliest infinite sequence of distinct nonnegative pairs of terms that interpenetrate to produce a prime number.
1
0, 11, 3, 17, 2, 23, 6, 13, 1, 21, 4, 19, 7, 27, 5, 33, 8, 39, 103, 10, 153, 20, 107, 12, 131, 15, 109, 16, 111, 26, 113, 24, 101, 30, 119, 14, 123, 25, 117, 29, 141, 22, 127, 18, 133, 31, 129, 28, 121, 34, 169, 36, 137, 32, 167, 38, 147, 35, 171, 43, 157, 37, 9, 41, 149, 44, 159, 55, 139, 46, 151, 45, 163, 48, 173, 42, 143, 51, 187, 49, 177, 52, 183, 50, 161, 54, 179, 47, 189
OFFSET
1,2
COMMENTS
The term a(n) must always be exactly one digit longer or shorter than the term a(n+1).
LINKS
Eric Angelini, Combs and Pharaohs, personal blog of the author.
EXAMPLE
Interpenetrate a(1) = 0 and a(2) = 11 to form 101 (a prime number);
interpenetrate a(2) = 11 and a(3) = 3 to form 131 (a prime number);
interpenetrate a(3) = 3 and a(4) = 17 to form 137 (a prime number);
interpenetrate a(4) = 17 and a(5) = 2 to form 127 (a prime number);
interpenetrate a(5) = 2 and a(6) = 23 to form 223 (a prime number);
interpenetrate a(6) = 23 and a(7) = 6 to form 263 (a prime number);
interpenetrate a(7) = 6 and a(8) = 13 to form 163 (a prime number);
interpenetrate a(8) = 13 and a(9) = 1 to form 113 (a prime number);
(...)
interpenetrate a(18) = 39 and a(19) = 103 to form 13093 (a prime number);
(...)
interpenetrate a(167) = 277 and a(168) = 1009 to form 1207079 (a prime number); etc.
MAPLE
Q:= proc(a, b) local La, Lb, i;
La:= convert(a, base, 10);
Lb:= convert(b, base, 10);
add(La[i]*10^(2*i-2), i=1..nops(La)) + add(Lb[i]*10^(2*i-1), i=1..nops(Lb))
end proc:
f:= proc(n) local d, x;
d:= 1+ilog10(n);
if n::odd then
for x from 10^(d-2) to 10^(d-1) - 1 do
if not(member(x, S)) and isprime(Q(n, x)) then return x fi
od
fi;
for x from 10^d+1 to 10^(d+1) - 1 by 2 do
if not(member(x, S)) and isprime(Q(x, n)) then return x fi
od;
FAIL
end proc:
R:= 0, 11: S:= {0, 11}: v:= 11:
for i from 2 to 100 do
v:= f(v);
R:= R, v;
S:= S union {v};
od:
R; # Robert Israel, Aug 22 2024
PROG
(Python)
from sympy import isprime
from itertools import islice
def ip(s, t): return int("".join(x+v for x, v in zip(s, t))+s[-1])
def agen(): # generator of terms
seen, an, found = set(), 0, True
while found:
yield an
seen.add(an)
s = str(an)
d, found = len(s), False
if s[-1] in "1379" and d > 1:
for k in range(10**(d-2), 10**(d-1)):
if k not in seen and isprime(ip(s, str(k))):
an, found = k, True
break
if not found:
for k in range(10**d, 10**(d+1)):
if k not in seen and isprime(ip(str(k), s)):
an, found = k, True
break
print(list(islice(agen(), 90))) # Michael S. Branicky, Aug 22 2024
CROSSREFS
Sequence in context: A088262 A110406 A237454 * A110434 A110798 A350246
KEYWORD
base,nonn,look
AUTHOR
STATUS
approved