A011539 -id:A011539 - cp's OEIS frontend

A283608 Numbers whose largest decimal digit is 5.

5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 105, 115, 125, 135, 145, 150, 151, 152, 153, 154, 155, 205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 305, 315, 325, 335, 345, 350, 351, 352, 353, 354, 355, 405, 415, 425, 435, 445, 450, 451, 452, 453, 454

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 5.
Number of terms less than 10^n is 6^n - 5^n.
Subsequence of A011535. - David A. Corneth, Mar 25 2017
Prime terms are in A106097.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A011535, A054055, A106097.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), this sequence (k = 5), A283609 (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=5); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 5];

Select[Range[1000], Max[IntegerDigits[#]] == 5 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==5, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

nxt(n) = {my(d = digits(n), i, j=0, t=0); forstep(i=#d,1,-1, if(d[i]!=5, j=i; break)); if(j>0, d[j]++; if(d[j]==5, for(k=j+1,#d,d[k]=0)); if(j<#d && d[j+1]==5, for(k=j+1,#d-1,d[k]=0)); for(k=1,j-1, if(d[k]==5,for(i=j+1, #d, d[i] = 0);break)), d = vector(#d+1); d[1]=1; d[#d]=5);sum(i=1, #d, d[i]*10^(#d-i))} \\ David A. Corneth, Mar 25 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==5]) # Indranil Ghosh, Mar 19 2017

A283609 Numbers whose largest decimal digit is 6.

Original entry on oeis.org

6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 106, 116, 126, 136, 146, 156, 160, 161, 162, 163, 164, 165, 166, 206, 216, 226, 236, 246, 256, 260, 261, 262, 263, 264, 265, 266, 306, 316, 326, 336, 346, 356, 360, 361, 362, 363, 364, 365, 366, 406, 416, 426

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 6.
Number of terms less than 10^n is 7^n - 6^n.
Prime terms are in A106096.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A054055, A106096.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), this sequence (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=6); # Muniru A Asiru, Mar 01 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 6]

Select[Range[1000], Max[IntegerDigits[#]] == 6 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==6, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==6]) # Indranil Ghosh, Mar 19 2017

A283610 Numbers n whose largest decimal digit is 7.

Original entry on oeis.org

7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 107, 117, 127, 137, 147, 157, 167, 170, 171, 172, 173, 174, 175, 176, 177, 207, 217, 227, 237, 247, 257, 267, 270, 271, 272, 273, 274, 275, 276, 277, 307, 317, 327, 337, 347, 357, 367, 370, 371, 372

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 7.
Number of terms less than 10^n is 8^n - 7^n.
Prime terms are in A106095.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A054055, A106095.

Cf. Sequences of numbers n whose largest decimal digit is k (for k = 1 - 9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), A283609 (k = 6), this sequence (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..380],n->Maximum(ListOfDigits(n))=7); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 7]

Select[Range[1000], Max[IntegerDigits[#]] == 7 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==7, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
[n for n in range(1, 401) if max(digits(n)[1:]) == 7]  # Indranil Ghosh, Mar 19 2017

A283611 Numbers whose largest decimal digit is 8.

Original entry on oeis.org

8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 108, 118, 128, 138, 148, 158, 168, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 208, 218, 228, 238, 248, 258, 268, 278, 280, 281, 282, 283, 284, 285, 286, 287, 288, 308, 318, 328, 338, 348

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 8.
Number of terms less than 10^n is 9^n - 8^n.
Prime terms are in A106094.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), A283609 (k = 6), A283610 (k = 7), this sequence (k = 8), A011539 (k = 9).

Filtered([1..400],n->Maximum(ListOfDigits(n))=8); # Muniru A Asiru, Mar 01 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 8]

f:= proc(n) local L;
  L:= convert(n,base,9);
  if not has(L,8) then return NULL fi;
  add(L[i]*10^(i-1),i=1..nops(L))
end proc:
map(f, [$8..1000]); # Robert Israel, Mar 27 2017

Select[Range@ 350, Max@ IntegerDigits@ # == 8 &] (* Michael De Vlieger, Mar 25 2017 *)

isok(n) = vecmax(digits(n)) == 8; \\ Michel Marcus, Mar 25 2017

A297418 a(n) is the smallest positive number not yet in the sequence that contains the largest digit in a(n-1); a(1)=0.

Original entry on oeis.org

0, 10, 1, 11, 12, 2, 20, 21, 22, 23, 3, 13, 30, 31, 32, 33, 34, 4, 14, 24, 40, 41, 42, 43, 44, 45, 5, 15, 25, 35, 50, 51, 52, 53, 54, 55, 56, 6, 16, 26, 36, 46, 60, 61, 62, 63, 64, 65, 66, 67, 7, 17, 27, 37, 47, 57, 70, 71, 72, 73, 74, 75, 76, 77, 78, 8, 18, 28, 38, 48, 58, 68, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 19, 29

Offset: 1

Enrique Navarrete, Dec 29 2017

Once the digit 9 is introduced in a(82)=89, all following terms must contain a 9.
The sequence contains no fixed points.
Analog sequence formed by taking the smallest digit from a(n-1) is A011540.

Robert G. Wilson v, Table of n, a(n) for n = 1..3000

Cf. A011539, A011540, A297352, A297353.

a[n_] := a[n] = Block[{k = 1, s = Union[ IntegerDigits[ a[n -1]]][[-1]], t = Array[a, n - 1]}, While[ MemberQ[t, k] || !MemberQ[ IntegerDigits@ k, s], k++]; k]; a[1] = 0; Array[a, 72] (* Robert G. Wilson v, Dec 30 2017 *)
Nest[Append[#, Block[{m = Max@ IntegerDigits@ Last@ #, k}, k = m; While[Nand[FreeQ[#, k], MemberQ[IntegerDigits[k], m]], k++]; k]] &, {0}, 84] (* Michael De Vlieger, Dec 30 2017 *)

first(n) = my(res = vector(n)); for(x=2, n, if(x == 2, res[x] = 10, for(i=1, +oo, if(!setsearch(Set(res), i) && setsearch(Set(digits(i)), vecmax(digits(res[x-1]))), res[x] = i; break())))); res \\ Iain Fox, Dec 31 2017

For n >= 91, a(n) = A011539(n - 81). - Iain Fox, Dec 31 2017

A245877 Primes p such that p - d and p + d are also primes, where d is the largest digit of p.

Original entry on oeis.org

263, 563, 613, 653, 1613, 1663, 3463, 4643, 5563, 5653, 6263, 6323, 12653, 13463, 14633, 16063, 16223, 21163, 21563, 25463, 26113, 30643, 32063, 33623, 36313, 41263, 41603, 44263, 53623, 54623, 56003, 60133, 61553, 62213, 62633, 64013, 65413, 105613, 106213

Offset: 1

Colin Barker, Aug 05 2014

Intersection of A245742 and A245743.
The largest digit of a(n) is 6, and the least significant digit of a(n) is 3.
Intersection of A006489, A011536, and complements of A011537, A011538, A011539. - Robert Israel, Aug 05 2014

			The prime 263 is in the sequence because 263 - 6 = 257 and 263 + 6 = 269 are both primes.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A006489, A245742, A245743, A245744, A245745, A245878.

pdpQ[n_]:=Module[{m=Max[IntegerDigits[n]]},AllTrue[n+{m,-m},PrimeQ]]; Select[ Prime[Range[11000]],pdpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 13 2017 *)

select(p->d=vecsort(digits(p),,4)[1]; isprime(p-d) && isprime(p+d), primes(20000))

import sympy
from sympy import prime
from sympy import isprime
for n in range(1,10**5):
  s=prime(n)
  lst = []
  for i in str(s):
    lst.append(int(i))
  if isprime(s+max(lst)) and isprime(s-max(lst)):
    print(s,end=', ')
# Derek Orr, Aug 13 2014

A043526 Numbers having two 9's in base 10.

Original entry on oeis.org

99, 199, 299, 399, 499, 599, 699, 799, 899, 909, 919, 929, 939, 949, 959, 969, 979, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 1099, 1199, 1299, 1399, 1499, 1599, 1699, 1799, 1899, 1909, 1919, 1929, 1939, 1949, 1959, 1969

Offset: 1

Clark Kimberling

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Subsequence of A011539.

Select[Range[2000],DigitCount[#,10,9]==2&] (* Harvey P. Dale, May 08 2018 *)

A043527 Numbers having three 9's in base 10.

Original entry on oeis.org

999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9099, 9199, 9299, 9399, 9499, 9599, 9699, 9799, 9899, 9909, 9919, 9929, 9939, 9949, 9959, 9969, 9979, 9989, 9990, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 10999

Offset: 1

Clark Kimberling

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Subsequence of A011539.

A043528 Numbers having four 9's in base 10.

Original entry on oeis.org

9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 90999, 91999, 92999, 93999, 94999, 95999, 96999, 97999, 98999, 99099, 99199, 99299, 99399, 99499, 99599, 99699, 99799, 99899, 99909, 99919, 99929, 99939

Offset: 1

Clark Kimberling

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Subsequence of A011539.

Select[Range[100000],DigitCount[#,10,9]==4&] (* Harvey P. Dale, Aug 22 2011 *)

A092361 Palindromic numbers containing one or more odd digits.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 232, 252, 272, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 414, 434, 454, 474, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 616, 636, 656, 676, 696

Offset: 1

Michael Joseph Halm, Mar 19 2004

Begins to differ from the odd palindromic numbers, A029950, in the 21st term.

			a(21) = 212 because it is the 21st palindromic number with an odd digit, the first even one

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A029950, A011539.

Select[Range[1000],PalindromeQ[#]&&AnyTrue[IntegerDigits[#],OddQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 24 2021 *)

Corrected and definition clarified by Harvey P. Dale, May 24 2021

cp's OEIS Frontend

A283608 Numbers whose largest decimal digit is 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

PARI

Python

A283609 Numbers whose largest decimal digit is 6.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

Python

A283610 Numbers n whose largest decimal digit is 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

Python

A283611 Numbers whose largest decimal digit is 8.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

A297418 a(n) is the smallest positive number not yet in the sequence that contains the largest digit in a(n-1); a(1)=0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A245877 Primes p such that p - d and p + d are also primes, where d is the largest digit of p.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A043526 Numbers having two 9's in base 10.

Views

Author