A158652 Any two consecutive digits in the sequence sum up to a prime.

1, 2, 3, 4, 7, 41, 43, 47, 49, 83, 85, 89, 202, 302, 303, 411, 412, 502, 503, 830, 2020, 2021, 2023, 2025, 2029, 2030, 2032, 3020, 3021, 4111, 4112, 5020, 5021, 6111, 6112, 9202, 9203, 20202, 30202, 30203, 41111, 41112, 50202, 50203, 83020, 202020

Offset

1,2

Comments

a(1)=1 and a(n) is always the smallest integer > a(n-1) not leading to a contradiction. Terms computed by M. F. Hasler.

From M. F. Hasler, Mar 24 2009: (Start)

After the initial 2,3,4,7,41,43,47,49,83,85,89, the following pattern repeats:

202,302,303,

411,412,502,503,830,

2020,2021,2023,2025,2029,2030,2032,3020,3021,

4111,4112,5020,5021,6111,6112,9202,9203,

with each time two extra digits (either 02 or 11):

20202,30202,30203,

41111,41112,50202,50203,83020,

202020,202021,202023,202025,202029,202030,202032,302020,302021,

411111,411112,502020,502021,611111,611112,920202,920203,

and so on. (End)

Links

Robert G. Wilson v, Table of n, a(n) for n=1..100

Eric Angelini, Chiffres consecutifs dans quelques suites

Eric Angelini, Chiffres consecutifs dans quelques suites [Cached copy, with permission]

Mathematica

f[s_List] := Block[{k = s[[ -1]] + 1, ls = Mod[ s[[ -1]], 10]}, While[ Union@ PrimeQ[ Plus @@@ Partition[ Join[{ls}, IntegerDigits@ k], 2, 1]] != {True}, k++ ]; Append[s, k]]; Nest[f, {1}, 45] (* Robert G. Wilson v, Apr 05 2009 *)

Prog

(Python)
from itertools import count, islice
allowed = {"0":"2357", "1":"1246", "2":"01359", "3":"0248", "4":"1379", "5":"0268", "6":"157", "7":"046", "8":"359", "9":"248"}
def cgen(seed, digits, geq="0"): # numbers satisfying the condition
    if digits == 1:
        yield from (c for c in allowed[seed] if c >= geq); return
    for f in (c for c in allowed[seed] if c >= geq):
        yield from (f + r for r in cgen(f, digits-1))
def nextc(k): # next element of cgen greater than k
    s = str(k)
    for d in count(len(s)):
        geq = s[0] if d == len(s) else "1"
        for c in map(int, cgen(s[-1], d, geq=geq)):
            if c > k: return c
def agen():
    an = 1
    for n in count(1): yield an; an = nextc(an)
print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 12 2022

Crossrefs

Cf. A152603-A152610.

Sequence in context: A094313 A214914 A070527 * A127074 A328322 A109617

Adjacent sequences: A158649 A158650 A158651 * A158653 A158654 A158655

Keyword

base,nonn

Author

Eric Angelini, Mar 23 2009

Status

approved