A106101 -id:A106101 - cp's OEIS frontend

A208270 Primes containing a digit 1.

11, 13, 17, 19, 31, 41, 61, 71, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 241, 251, 271, 281, 311, 313, 317, 331, 401, 419, 421, 431, 461, 491, 521, 541, 571, 601, 613, 617, 619, 631, 641, 661

Offset: 1

Jaroslav Krizek, Mar 04 2012

Subsequence of A011531, A062634, A092911 and A092912.
Supersequence of A106101, A045707 and A030430.
Complement of A208271 with respect to A011531.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for sequences related to decimal expansion of n

Cf. A208271 (nonprimes containing a digit 1), A011531 (numbers containing a digit 1).

Complement of A038603 in A000040. - M. F. Hasler, Mar 05 2012

[p: p in PrimesUpTo(400) | 1 in Intseq(p)]; // Vincenzo Librandi, Apr 29 2019

Select[Prime[Range[124]], MemberQ[IntegerDigits[#], 1] &](* Jayanta Basu, Apr 01 2013 *)
Select[Prime[Range[200]],DigitCount[#,10,1]>0&] (* Harvey P. Dale, Dec 15 2020 *)

forprime(p=2,1e3,s=vecsort(eval(Vec(Str(p))),,8);if(s[1]==1||(s[1]==0&&s[2]==1),print1(p", "))) \\ Charles R Greathouse IV, Mar 04 2012

is_A208270(n)=isprime(n)&setsearch(Set(Vec(Str(n))),1) \\ M. F. Hasler, Mar 05 2012

a(n) ~ n log n since the sequence contains almost all primes. - Charles R Greathouse IV, Mar 04 2012

A284062 Numbers whose smallest decimal digit is 1.

Original entry on oeis.org

1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers k such that A054054(k) = 1.

Prime terms are in A106101.

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), this sequence (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), A284069 (k = 8), A002283 (k = 9).

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

Select[Range[300], Min[IntegerDigits[#]]==1 &] (* Indranil Ghosh, Mar 19 2017 *)

for(n=1, 300, if(vecmin(digits(n))==1, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 301) if min(digits(n)[1:])==1]) # Indranil Ghosh, Mar 19 2017

A206159 Numbers needing at most two digits to write all positive divisors in decimal representation.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 17, 19, 22, 31, 33, 41, 55, 61, 71, 77, 101, 113, 121, 131, 151, 181, 191, 199, 211, 311, 313, 331, 661, 811, 881, 911, 919, 991, 1111, 1117, 1151, 1171, 1181, 1511, 1777, 1811, 1999, 2111, 2221, 3313, 3331, 4111, 4441, 6661, 7177, 7717, 8111, 9199, 10111, 11113

Offset: 1

Reinhard Zumkeller, Feb 05 2012

The terms of A203897 having all divisors in A020449 (in particular, the first 1022 terms) are a subsequence. - M. F. Hasler, May 02 2022

Since 1 and the term itself are divisors, one must only check repdigits and those containing only 1 and another digit. - Michael S. Branicky, May 02 2022

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..500 from M. F. Hasler)

Cf. A027750, A031955, A011531, A106101, A004022, A062634.

Cf. A203897 (an "almost subsequence"), A020449 (primes with only digits 0 & 1), A095048 (number of distinct digits in divisors(n)).

Select[Range[12000],Length[Union[Flatten[IntegerDigits/@Divisors[#]]]]<3&] (* Harvey P. Dale, May 03 2022 *)

select( {is_A206159(n)=#Set(concat([digits(d)|d<-divisors(n)]))<3}, [1..10^4]) \\ M. F. Hasler, May 02 2022

from sympy import divisors
def ok(n):
    digits_used = set()
    for d in divisors(n, generator=True):
        digits_used |= set(str(d))
        if len(digits_used) > 2: return False
    return True
print([k for k in range(1, 9000) if ok(k)]) # Michael S. Branicky, May 02 2022

A095048(a(n)) <= 2.

Terms corrected by Harvey P. Dale, May 02 2022

Edited by N. J. A. Sloane, May 02 2022

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A208270 Primes containing a digit 1.

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A284062 Numbers whose smallest decimal digit is 1.

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A206159 Numbers needing at most two digits to write all positive divisors in decimal representation.

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