A050289 -id:A050289 - cp's OEIS frontend

A358097 a(n) is the smallest integer m > n such that m and n have no common digit, or -1 when such integer m does not exist.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 20, 30, 20, 20, 20, 20, 20, 20, 20, 31, 30, 30, 40, 30, 30, 30, 30, 30, 30, 41, 40, 40, 40, 50, 40, 40, 40, 40, 40, 51, 50, 50, 50, 50, 60, 50, 50, 50, 50, 61, 60, 60, 60, 60, 60, 70, 60, 60, 60, 71, 70, 70, 70, 70, 70, 70, 80, 70, 70, 81, 80, 80, 80, 80

Offset: 0

Bernard Schott, Oct 29 2022

When n is pandigital with or without 0 (A050278, A050289, A171102), m does not exist, so a(n) = -1; see examples for smallest pandigital cases.

			a(10) = 22; a(11) = 20; a(12) = 30.
a(123456789) = -1; a(1234567890) = -1.

Michel Marcus, Table of n, a(n) for n = 0..10000

Cf. A002275, A050278, A050289, A171102.
Cf. A030283 (trajectory starting 0).
Cf. A358098 (similar, with largest integer m < n).

a[n_] := Module[{d = Complement[Range[0, 9], IntegerDigits[n]], m = n + 1}, If[d == {} || d == {0}, -1, While[! AllTrue[IntegerDigits[m], MemberQ[d, #] &], m++]; m]]; Array[a, 100, 0] (* Amiram Eldar, Oct 29 2022 *)

isfull(d) = my(dd=setminus([0..9], d)); (dd==[]) || (dd==[0]);
a(n) = my(d=Set(digits(n))); if (isfull(d), -1, my(k=n+1); while (#setintersect(Set(digits(k)), d), k++); k); \\ Michel Marcus, Oct 29 2022

from itertools import count, product
def a(n):
    s = str(n)
    r = sorted(set("1234567890") - set(s))
    if len(r) == 0 or r == ["0"]: return -1
    for d in count(len(s)):
        for p in product(r, repeat=d):
            m = int("".join(p))
            if m > n: return m
print([a(n) for n in range(75)]) # Michael S. Branicky, Oct 29 2022

a(10^n-k) = 10^n when n >= 2 and 1 <= k <= 8.

a(10^n) = 2 * A002275(n+1), when n >= 1.

A358098 a(n) is the largest integer m < n such that m and n have no common digit, or -1 when such integer m does not exist.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 19, 9, 19, 19, 19, 19, 19, 19, 19, 18, 29, 29, 19, 29, 29, 29, 29, 29, 29, 28, 39, 39, 39, 29, 39, 39, 39, 39, 39, 38, 49, 49, 49, 49, 39, 49, 49, 49, 49, 48, 59, 59, 59, 59, 59, 49, 59, 59, 59, 58, 69, 69, 69, 69, 69, 69, 59, 69, 69, 68, 79

Offset: 1

Bernard Schott, Oct 29 2022

Note that only when n is pandigital with 0 (A050278, A171102), such m does not exist and a(n) = -1; see examples for smallest pandigital cases.

			a(19) = 8, a(20) = 19; a(21) = 9.
a(123456789) = 0; a(1234567890) = -1.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A050289, A050278, A171102.

Cf. A358097 (similar, with smallest integer m > n).

a[n_] := Module[{d = Complement[Range[0, 9], IntegerDigits[n]], m = n - 1}, If[d == {} || d == {0}, -1, While[m >= 0 && ! AllTrue[IntegerDigits[m], MemberQ[d, #] &], m--]; m]]; Array[a, 100] (* Amiram Eldar, Oct 29 2022 *)

a(n) = my(d=Set(digits(n))); forstep (m=n-1, 0, -1, if (!#setintersect(d, Set(digits(m))), return(m))); return(-1); \\ Michel Marcus, Oct 30 2022

from itertools import product
def a(n):
    s = str(n)
    r = sorted(set("1234567890") - set(s), reverse=True)
    if len(r) == 0: return -1
    if r == ["0"]: return 0
    for d in range(len(s), 0, -1):
        for p in product(r, repeat=d):
            m = int("".join(p))
            if m < n: return m
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Oct 29 2022

a(10^n) = 10^n - 1 for n >= 0.

a(A050289(n))=0.

A113640 Zeroless pandigital strong pseudoprimes (base-2).

Original entry on oeis.org

6913548721, 11396574289, 13842496537, 14872531669, 16952474813, 16963825147, 16974152381, 18632427859, 27569184173, 28239546721, 47569352881, 54689213377, 54987116329, 68719214593, 79633524181, 93541462873, 95126134837, 118214685793, 121899457633, 123572846953

Offset: 1

Shyam Sunder Gupta, Jan 15 2006

			a(1) = 6913548721 is a term because 6913548721 is a strong pseudoprime (base-2) and also contains all digits from 1 to 9 so it is also zeroless pandigital.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A050289 and A001262.

More terms from Amiram Eldar, Nov 10 2019

A113641 Zeroless pandigital pseudoprimes (base-2).

Original entry on oeis.org

1267834459, 1957283461, 2449856317, 2452396871, 2459637181, 2523476981, 3815417629, 4176385921, 4357289761, 4682134579, 5748693121, 6913548721, 7531426981, 7693527841, 8129734561, 9146572381, 9752463781, 11396574289, 12679888453, 13842496537, 13946829751, 14872531669

Offset: 1

Shyam Sunder Gupta, Jan 15 2006

			a(1) = 1267834459 is a term because 1267834459 is a pseudoprime (base-2) and also contain all digits from 1 to 9 so zeroless pandigital also.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A050289 and A001567.

More terms from Amiram Eldar, Nov 10 2019

A113644 Zeroless pandigital Carmichael numbers.

Original entry on oeis.org

5748693121, 9146572381, 13946829751, 15989367241, 28239546721, 28637914561, 36976452481, 73487592361, 79623874561, 92437591681, 95287763341, 121254376891, 129855637441, 149378245633, 189634571281, 195376852441

Offset: 1

Shyam Sunder Gupta, Jan 15 2006

			a(1) = 5748693121 is a term because 5748693121 is a Carmichael number and also contains all the digits from 1 to 9, so it is also a zeroless pandigital number.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A002997 and A050289.

A159568 Zeroless pandigital emirps.

Original entry on oeis.org

1123564987, 1123586479, 1123869547, 1124356789, 1124378659, 1124685973, 1124698537, 1124753689, 1124763589, 1124785639, 1124879563, 1124895367, 1124896753, 1124956837, 1124978563, 1125347689, 1125386749, 1125398467, 1125487963, 1125648379, 1125748693

Offset: 1

Lekraj Beedassy, Apr 15 2009

There are 56104 10-digit terms. - Jud McCranie, Jul 01 2013

Jud McCranie, Table of n, a(n) for n = 1..1000

Cf. A050290, A050289.

Corrected and more terms added by Jud McCranie, Jul 01 2013

A241528 Primes p such that p + 1234567890 is also prime where 1234567890 is the first pandigital number with digits in order.

Original entry on oeis.org

17, 23, 37, 59, 131, 139, 157, 199, 241, 311, 353, 359, 397, 433, 479, 547, 673, 691, 769, 877, 937, 947, 953, 1051, 1091, 1097, 1181, 1297, 1301, 1409, 1451, 1471, 1489, 1531, 1609, 1619, 1697, 1709, 1861, 1879, 1889, 1913, 1951, 2053, 2063, 2089, 2099, 2113

Offset: 1

K. D. Bajpai, Apr 25 2014

nonn

			17 is prime and appears in the sequence because 17 + 1234567890 = 1234567907, which is also prime.
23 is prime and appears in the sequence because 23 + 1234567890 = 1234567913, which is also prime.
19 is prime but not included in the sequence since 19 + 1234567890 = 1234567909 = (59107)*(20887), which is not prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A002496, A028871, A050289, A056899, A234812, A235640, A240587.

KD := proc() local a,k; k:=ithprime(n);a:=k+1234567890; if isprime(a) then RETURN (k); fi; end: seq(KD(), n=1..1000);

lst={}; Do[p=Prime[n]; If[PrimeQ[p+1234567890], AppendTo[lst,p]],{n,1,1000}]; lst
(* For the b-file *)  c=0; k=Prime[n]; a=k+1234567890; Do[If[PrimeQ[a], c++; Print[c," ",k]],{n,1,10^5}]
Select[Prime[Range[400]],PrimeQ[#+1234567890]&] (* Harvey P. Dale, Nov 18 2021 *)

s=[]; forprime(p=2, 3000, if(isprime(p+1234567890), s=concat(s, p))); s \\ Colin Barker, Apr 25 2014

A241537 Cubes c such that c + 1234567890 is prime where 1234567890 is the first pandigital number with digits in order.

Original entry on oeis.org

1, 50653, 79507, 456533, 571787, 1295029, 1685159, 1771561, 2248091, 2685619, 3307949, 4173281, 7880599, 9393931, 10218313, 10793861, 11697083, 17373979, 18191447, 22665187, 30664297, 47045881, 70444997, 111284641, 146363183, 151419437, 156590819, 192100033

Offset: 1

K. D. Bajpai, Apr 25 2014

nonn

			50653 = 37^3 and appears in the sequence because 50653 + 1234567890 = 1234618543, which is prime.
79507 = 43^3  and appears in the sequence because 79507 + 1234567890 = 1234647397, which is prime.
64000 = 40^3 but not included in the sequence since 64000 + 1234567890 = 1234631890 = (2)*(5)*(29389)*(4201), which is not prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A002496, A028871, A050289, A056899, A234812, A235640, A240587.

KD := proc() local a,c; c:=n^3;a:=c+1234567890; if isprime(a) then RETURN (c); fi; end: seq(KD(), n=1..1000);

lst={}; Do[c=n^3; If[PrimeQ[c+1234567890], AppendTo[lst,c]], {n,1,1000}]; lst
(*For the b-file*)  m=0; c=n^3; a=c+1234567890; Do[If[PrimeQ[a],m++; Print[m," ",c]], {n,1,4*10^5}]

s=[]; for(n=1, 1000, c=n^3; if(isprime(c+1234567890), s=concat(s, c))); s \\ Colin Barker, Apr 25 2014

A241538 Squares s such that s + 1234567890 is prime.

Original entry on oeis.org

1, 169, 1681, 6889, 8281, 11881, 24649, 27889, 41209, 57121, 58081, 67081, 80089, 101761, 124609, 175561, 185761, 201601, 212521, 332929, 380689, 413449, 461041, 508369, 534361, 609961, 625681, 654481, 683929, 693889, 822649, 829921, 833569, 1014049, 1018081

Offset: 1

K. D. Bajpai, Apr 25 2014

1234567890 is the first pandigital number with digits in order.

			169 = 13^2 and appears in the sequence because 169 + 1234567890 = 1234568059, which is prime.
1681 = 41^2  and appears in the sequence because 1681 + 1234567890 = 1234569571, which is prime.
625 = 25^2 but is not included in the sequence since 625 + 1234567890 = 1234568515 = (5)*(246913703), which is not prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A002496, A028871, A050289, A056899, A234812, A235640, A240587.

KD := proc() local a,s; s:=n^2;a:=s+1234567890; if isprime(a) then RETURN (s); fi; end: seq(KD(), n=1..2000);

A241538 = {}; Do[s = n^2; If[PrimeQ[s + 1234567890], AppendTo[A241538, s]], {n, 2000}]; A241538
(* For the b-file *) c = 0; s = n^2; a = s + 1234567890; Do[If[PrimeQ[a], c++; Print[c, " ", s]], {n, 4*10^5}] (* Bajpai *)
Select[Range[1000]^2, PrimeQ[# + 1234567890] &] (* Alonso del Arte, Apr 25 2014 *)

A323026 Zeroless pandigital numbers that are between two twin primes.

Original entry on oeis.org

123457968, 123459768, 123946578, 124397658, 124936578, 124953678, 125347698, 125437968, 125463798, 125674398, 126345978, 126495738, 126593478, 126597348, 126945738, 127394568, 127396458, 127453968, 127459638, 127659438, 129357648, 129635478, 129673548, 132564978, 132594768, 132769458

Offset: 1

Pierandrea Formusa, Jan 02 2019

Intersection of A050289 and A014574.
The definition permits repeated digits. - N. J. A. Sloane, May 16 2023
a(n) mod 10 is either 2 or 8. First term with a(n) mod 10 = 2 is a(27) = 134756982. - Chai Wah Wu, Jan 27 2019
There are 2595 terms that are pandigital without repeating any digit. - Harvey P. Dale, Jan 25 2021

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A050289 (zeroless pandigital numbers), A014574 (average of twin primes).

isok(n) = my(d=digits(n)); vecmin(d) && (#Set(d)==9) && isprime(n-1) && isprime(n+1);
for (n=123456789, 133000000, if (isok(n), print1(n, ", "))) \\ Michel Marcus, Jan 04 2019

import itertools
from sympy import isprime
nmax=pow(10,10)
r=""
li=[]
def is_pandigit_easy(n):
    l=[]
    s=str(n)
    if '0' in s: return(False)
    for ch in s:
        if ch not in l: l.append(ch)
    l=list(set(l))
    if len(l)==9:
        return(True)
    else:
        return(False)
t=0
tmax=50
for i in range(123456789,nmax):
    if is_pandigit_easy(i):
        if isprime(i-1) and isprime(i+1):
            li.append(i)
            t+=1
            if t>tmax: break
first_elem=26
for k in li[:first_elem]:
      r=r+","+str(k)
print(r[1:])

from itertools import permutations
from sympy import isprime
A323026_list = [n for n in (int(''.join(s)) for s in permutations('123456789')) if isprime(n-1) and isprime(n+1)] # Chai Wah Wu, Jan 27 2019

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A358097 a(n) is the smallest integer m > n such that m and n have no common digit, or -1 when such integer m does not exist.

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A358098 a(n) is the largest integer m < n such that m and n have no common digit, or -1 when such integer m does not exist.

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A113640 Zeroless pandigital strong pseudoprimes (base-2).

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A113641 Zeroless pandigital pseudoprimes (base-2).

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A113644 Zeroless pandigital Carmichael numbers.

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A159568 Zeroless pandigital emirps.

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A241528 Primes p such that p + 1234567890 is also prime where 1234567890 is the first pandigital number with digits in order.

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A241537 Cubes c such that c + 1234567890 is prime where 1234567890 is the first pandigital number with digits in order.

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