A068863 -id:A068863 - cp's OEIS frontend

A068868 Numbers prime(k) such that A068863(k) = prime(k).

2, 3, 5, 7, 11, 17, 37, 41, 47, 61, 101, 107, 331, 443, 463, 563, 853, 859, 1049, 2819, 7229, 9241, 10799, 10837, 31123, 31177, 51133, 51151, 71069, 91297, 111211, 289031, 511177, 689233, 689257, 689267, 689291, 889349, 889363, 911171, 911179, 1109477

Offset: 1

Amarnath Murthy, Mar 13 2002

Cf. A068853, A068863.

Definition corrected. More terms from b068863.txt. - R. J. Mathar, Nov 25 2015

Missing 41 and 47 inserted and corrections arising from incorrect b-file in A068863 and more terms from Sean A. Irvine, Mar 19 2024

A068861 a(1) = 1; a(n+1) is the smallest number not already in the sequence which differs from a(n) at every digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 12, 20, 11, 22, 13, 24, 15, 23, 14, 25, 16, 27, 18, 26, 17, 28, 19, 30, 29, 31, 40, 32, 41, 33, 42, 34, 43, 35, 44, 36, 45, 37, 46, 38, 47, 39, 48, 50, 49, 51, 60, 52, 61, 53, 62, 54, 63, 55, 64, 56, 65, 57, 66, 58, 67, 59, 68, 70, 69, 71, 80

Offset: 1

Amarnath Murthy, Mar 13 2002

			11 follows 20 as the smallest number not included earlier and differing at every digit position.

Paul Tek, Table of n, a(n) for n = 1..10000

Cf. A068860, A068863.

Cf. A067581.

import Data.List (delete)
a068861 n = a068861_list !! (n-1)
a068861_list = f "x" (map show [1..]) where
   f u us = g us where
     g (v:vs)
       | and $ zipWith (/=) u v = (read v :: Int) : f v (delete v us)
       | otherwise = g vs
-- Reinhard Zumkeller, Dec 21 2013

A068853 a(1) = 2; a(n+1) is the smallest prime > a(n) which differs from it in every digit.

Original entry on oeis.org

2, 3, 5, 7, 11, 23, 31, 43, 59, 61, 73, 89, 97, 101, 223, 307, 419, 503, 617, 701, 823, 907, 1013, 2129, 3001, 4127, 5003, 6121, 7013, 8101, 9013, 10139, 21001, 30113, 41039, 50101, 61027, 70111, 81023, 90107, 101021, 210109, 301013, 410141, 501013, 610157, 701009

Offset: 1

Amarnath Murthy, Mar 12 2002

a(8996) has 1001 digits. - Michael S. Branicky, Mar 19 2024

			223 is a member and the next few primes are 227, 229, ... 283, 297, 307. 307 is the smallest one which differs from 223 in all corresponding positions.

Michael S. Branicky, Table of n, a(n) for n = 1..8995

Cf. A068863.

from sympy import isprime
from itertools import count, islice, product
def diffgen(n): # generator of numbers >n sharing no digits with n
    s = str(n)
    P = [list(str(d) for d in range(10) if str(d) != si) for si in s]
    if s[0] < '9':
        f = [d for d in P[0] if d > s[0]]
        for t in product(*([f]+P[1:])):
            yield int("".join(t))
    for e in count(1):
        for t in product("123456789", *(["0123456789"]*(e-1) + P)):
            yield int("".join(t))
def agen(): # generator of terms
    an = 2
    while True:
        yield an
        an = next(k for k in diffgen(an) if isprime(k))
print(list(islice(agen(), 47))) # Michael S. Branicky, Mar 19 2024

Corrected and extended by Ray Chandler, Jul 19 2003

a(46) and beyond from Michael S. Branicky, Mar 19 2024

A284146 a(n+1) is the smallest prime not already in the sequence which shares no digit with a(n).

Original entry on oeis.org

2, 3, 5, 7, 11, 23, 17, 29, 13, 47, 19, 37, 41, 53, 61, 43, 59, 31, 67, 83, 71, 89, 73, 101, 79, 103, 97, 113, 227, 109, 223, 107, 229, 131, 257, 139, 277, 149, 233, 151, 239, 157, 263, 179, 283, 167, 293, 181, 269, 137, 409, 127, 349

Offset: 1

Zak Seidov, Mar 20 2017

nonn

The sequence is not a permutation of prime numbers.
E.g., after calculating 2001 terms of the sequence, the first absent primes  are 1973,3719,3917,7193,9137,9173,9371. It's evident that these numbers will never appear in the sequence because any last  term of the sequence should use at least one of digits 1,3,7,9.
The first nine terms {2, 3, 5, 7, 11, 23, 17, 29, 13} coincide with A068863(1..9).
The only fixed points are a(n) for n={1, 2, 3, 4, 5, 7, 12, 13, 17, 19} are {2, 3, 5, 7, 11, 17, 37, 41, 59, 67} that is for these n's a(n)=prime(n)=A000040(n).
a (100*k) for k = 1,20: {443, 1193, 1741, 1621, 4567, 6047, 5851, 6491, 7151, 7559, 9349, 10601, 11119, 11699, 13001, 11839, 14107, 16111, 15073, 16487}.

Giovanni Resta, Table of n, a(n) for n = 1..10000
Zak Seidov, Graph of first 2000 terms.

Cf. A000040, A068863, A067581, A107801.

a = {2}; While[ Length[a] < 100, d = IntegerDigits@ Last@ a; p = 2; While[ Intersection[ IntegerDigits@p, d] != {} || MemberQ[a, p], p = NextPrime@ p]; AppendTo[a, p]]; a (* Giovanni Resta, Mar 21 2017 *)

cp's OEIS Frontend

A068868 Numbers prime(k) such that A068863(k) = prime(k).

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A068861 a(1) = 1; a(n+1) is the smallest number not already in the sequence which differs from a(n) at every digit.

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A068853 a(1) = 2; a(n+1) is the smallest prime > a(n) which differs from it in every digit.

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A284146 a(n+1) is the smallest prime not already in the sequence which shares no digit with a(n).

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Mathematica