cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 14 results. Next

A235154 Primes which have one or more occurrences of exactly two different digits.

Original entry on oeis.org

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 113, 131, 151, 181, 191, 199, 211, 223, 227, 229, 233, 277, 311, 313, 331, 337, 353, 373, 383, 433, 443, 449, 499, 557, 577, 599, 661, 677, 727, 733, 757, 773, 787, 797, 811
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 101.
a(3402) > 10^10.

Links

Crossrefs

Cf. A034845, A235155-A235161, A030291.

Programs

  • PARI
    s=[]; forprime(n=10, 1000, if(#vecsort(eval(Vec(Str(n))),,8)==2, s=concat(s, n))); s
  • PARI
    is(n)=isprime(n) && #Set(digits(n))==2 \\ Charles R Greathouse IV, Feb 23 2017
  • PARI
    \\ See Corneth link
  • Python
    from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
from itertools import count, islice, combinations_with_replacement, product
def agen():
    for digits in count(2):
        s = set()
        for pair in product("0123456789", "1379"):
            if pair[0] == pair[1]: continue
            for c in combinations_with_replacement(pair, digits):
                if len(set(c)) < 2 or sum(int(ci) for ci in c)%3 == 0:
                    continue
                for p in multiset_permutations(c):
                    if p[0] == "0": continue
                    t = int("".join(p))
                    if isprime(t):
                        s.add(t)
        yield from sorted(s)
print(list(islice(agen(), 100))) # Michael S. Branicky, Jan 23 2022

A235690 Semiprimes which have one or more occurrences of exactly two different digits.

Original entry on oeis.org

10, 14, 15, 21, 25, 26, 34, 35, 38, 39, 46, 49, 51, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 115, 118, 119, 121, 122, 133, 141, 155, 161, 166, 177, 202, 221, 226, 262, 299, 303, 323, 334, 335, 339, 355, 377, 393, 411, 422, 445, 446, 447, 454
Offset: 1

Views

Author

Colin Barker, Jan 14 2014

Keywords

Comments

The first term having a repeated digit is 115.

Examples

			1000000000010101 is a term because it is made of the digits 0 and 1 and it is the product of the two primes 18463559 and 54160739.

Crossrefs

Cf. A235691-A235696.
Cf. A235154-A235161.

Programs

  • Mathematica
    Select[Range[454], Length@Union@ IntegerDigits[#] == 2 && Total[Last /@ FactorInteger[#]] == 2 &] (* Giovanni Resta, Jan 14 2014 *)
  • PARI
    list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, listput(v, t*q))); vecsort(Vec(v)) \\ From A001358
b=list(10000); s=[]; for(n=1, #b, if(#vecsort(eval(Vec(Str(b[n]))),,8)==2, s=concat(s, b[n]))); s

A235696 Semiprimes which have one or more occurrences of exactly eight different digits.

Original entry on oeis.org

10234569, 10234657, 10234685, 10234687, 10234769, 10234795, 10234859, 10234865, 10234879, 10234957, 10234967, 10235469, 10235479, 10235489, 10235497, 10235679, 10235689, 10235769, 10235789, 10235798, 10235846, 10235847, 10235879, 10235894, 10235947, 10235986
Offset: 1

Views

Author

Colin Barker, Jan 14 2014

Keywords

Links

Crossrefs

Cf. A235690-A235695.
Cf. A235154-A235161.

Programs

  • Mathematica
    Select[Range[10234000,10236000],PrimeOmega[#]==Count[DigitCount[#],0]==2&] (* Harvey P. Dale, Sep 01 2014 *)
  • PARI
    list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, listput(v, t*q))); vecsort(Vec(v)) \\ From A001358
b=list(1030000); s=[]; for(n=1, #b, if(#vecsort(eval(Vec(Str(b[n]))),,8)==8, s=concat(s, b[n]))); s

A235155 Primes which have one or more occurrences of exactly three different digits.

Original entry on oeis.org

103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 317, 347, 349, 359, 367, 379, 389, 397, 401, 409, 419, 421, 431, 439, 457, 461, 463, 467, 479, 487, 491, 503, 509, 521, 523, 541, 547
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 1009.

Links

Crossrefs

Cf. A235154, A235156, A235157, A235158, A235159, A235160, A235161.
Cf. A074675.

Programs

  • MATLAB
    %See Conrey Link
  • Mathematica
    Select[Prime[Range[200]],Count[DigitCount[#],0]==7&] (* Harvey P. Dale, Jul 27 2020 *)
  • PARI
    s=[]; forprime(n=100, 1000, if(#vecsort(eval(Vec(Str(n))),,8)==3, s=concat(s, n))); s

A235157 Primes which have one or more occurrences of exactly five different digits.

Original entry on oeis.org

10243, 10247, 10253, 10259, 10267, 10273, 10289, 10357, 10369, 10427, 10429, 10453, 10457, 10459, 10463, 10487, 10529, 10567, 10589, 10597, 10627, 10639, 10657, 10687, 10723, 10729, 10739, 10753, 10789, 10837, 10847, 10853, 10859, 10867, 10937, 10957
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 100237.
There are 2,529 5-digit primes in the sequence. Harvey P. Dale, Feb 06 2015

Links

Crossrefs

Cf. A235154-A235156, A235158-A235161.
Cf. A074671.

Programs

  • Mathematica
    Select[Prime[Range[1255,1355]],Max[DigitCount[#]]==1&] (* The program is only accurate for 5-digit primes, of which there are 2529 satisfying the definition *) (* Harvey P. Dale, Feb 06 2015 *)
  • PARI
    s=[]; forprime(n=10000, 13000, if(#vecsort(eval(Vec(Str(n))),,8)==5, s=concat(s, n))); s

A235158 Primes which have one or more occurrences of exactly six different digits.

Original entry on oeis.org

102359, 102367, 102397, 102437, 102497, 102539, 102547, 102563, 102587, 102593, 102643, 102647, 102653, 102673, 102679, 102763, 102769, 102793, 102859, 102953, 102967, 102983, 103289, 103457, 103529, 103549, 103567, 103657, 103687, 103769, 103867, 103967
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 1002347.

Links

Crossrefs

Cf. A074669, A235154-A235157, A235159-A235161.

Programs

  • PARI
    s=[]; forprime(n=100000, 105000, if(#vecsort(eval(Vec(Str(n))),,8)==6, s=concat(s, n))); s

A235159 Primes which have one or more occurrences of exactly seven different digits.

Original entry on oeis.org

1023467, 1023487, 1023697, 1023769, 1023857, 1023947, 1024357, 1024379, 1024579, 1024589, 1024693, 1024697, 1024783, 1024853, 1024957, 1024963, 1024987, 1025347, 1025483, 1025693, 1025749, 1025789, 1025839, 1025873, 1025897, 1026359, 1026439, 1026457
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 10023649.

Links

Crossrefs

Cf. A074667, A235154-A235158, A235160, A235161.

Programs

  • Mathematica
    Select[Prime[Range[PrimePi[102*10^4],PrimePi[103*10^4]]],Count[ DigitCount[ #],0] ==3&] (* Harvey P. Dale, Mar 21 2018 *)
  • PARI
    s=[]; forprime(n=1000000, 1030000, if(#vecsort(eval(Vec(Str(n))),,8)==7, s=concat(s, n))); s

A235160 Primes which have one or more occurrences of exactly eight different digits.

Original entry on oeis.org

10234589, 10234759, 10234897, 10235647, 10235749, 10235867, 10236547, 10236857, 10237849, 10238467, 10238597, 10238647, 10238759, 10238957, 10239487, 10239587, 10239847, 10243567, 10243657, 10243759, 10243769, 10243867, 10243897, 10245397
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 100234657.

Links

Crossrefs

Cf. A074665, A235154-A235159, A235161.

Programs

  • Mathematica
    Select[Prime[Range[664580,68*10^4]],Count[DigitCount[#],0]==2&] (* Harvey P. Dale, Apr 05 2019 *)
  • PARI
    s=[]; forprime(n=10000000, 10250000, if(#vecsort(eval(Vec(Str(n))),,8)==8, s=concat(s, n))); s

A235691 Semiprimes which have one or more occurrences of exactly three different digits.

Original entry on oeis.org

106, 123, 129, 134, 142, 143, 145, 146, 158, 159, 169, 178, 183, 185, 187, 194, 201, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 235, 237, 247, 249, 253, 254, 259, 265, 267, 274, 278, 287, 289, 291, 295, 298, 301, 302, 305, 309, 314, 319, 321, 326, 327
Offset: 1

Views

Author

Colin Barker, Jan 14 2014

Keywords

Comments

The first term having a repeated digit is 1003.

Examples

			91119111691966691969 is a term, because it is made of the 3 digits {1, 6, 9} and is the product of two primes 9397848521 and 9695741689. - _Giovanni Resta_, Jan 14 2014

Crossrefs

Cf. A235690, A235692-A235696.
Cf. A235154-A235161.

Programs

  • Mathematica
    Select[Range@999, Length@ Union@ IntegerDigits[#] == 3 && Total[Last /@ FactorInteger[#]] == 2 &] (* Giovanni Resta, Jan 14 2014 *)
  • PARI
    list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, listput(v, t*q))); vecsort(Vec(v)) \\ From A001358
b=list(10000); s=[]; for(n=1, #b, if(#vecsort(eval(Vec(Str(b[n]))),,8)==3, s=concat(s, b[n]))); s

A235156 Primes which have one or more occurrences of exactly four different digits.

Original entry on oeis.org

1039, 1049, 1063, 1069, 1087, 1093, 1097, 1237, 1249, 1259, 1279, 1283, 1289, 1297, 1307, 1327, 1367, 1409, 1423, 1427, 1429, 1439, 1453, 1459, 1483, 1487, 1489, 1493, 1523, 1543, 1549, 1567, 1579, 1583, 1597, 1607, 1609, 1627, 1637, 1657, 1693, 1697, 1709
Offset: 1

Views

Author

Colin Barker, Jan 04 2014

Keywords

Comments

The first term having a repeated digit is 10037.

Links

Crossrefs

Cf. A235154, A235155, A235157-A235161.
Cf. A074673.

Programs

  • PARI
    s=[]; forprime(n=1000, 2000, if(#vecsort(eval(Vec(Str(n))),,8)==4, s=concat(s, n))); s
Showing 1-10 of 14 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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