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 1-7 of 7 results.

A383978 Primes with at least two identical trailing digits.

Original entry on oeis.org

11, 199, 211, 233, 277, 311, 433, 499, 577, 599, 677, 733, 811, 877, 911, 977, 1033, 1277, 1399, 1433, 1499, 1511, 1699, 1733, 1777, 1811, 1877, 1933, 1999, 2011, 2099, 2111, 2311, 2333, 2377, 2399, 2411, 2477, 2633, 2677, 2699, 2711, 2777, 2833, 2999, 3011, 3299
Offset: 1

Views

Author

Stefano Spezia, May 16 2025

Keywords

Links

Crossrefs

Cf. A131306, A383979, A384013, A384015.
Subsequence of A050758.
Cf. A061022 (variant).

Programs

  • Maple
    select(isprime, [seq(seq(i*100 + j*11, j = [1,3,7,9]),i=0..100)]); # Robert Israel, May 17 2025
  • Mathematica
    Select[Prime[Range[500]],Part[d=IntegerDigits[#],l=IntegerLength[#]]==Part[d,l-1] &]
  • Python
    from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from filter(isprime, (i+k for i in count(0, 100) for k in (11, 33, 77, 99)))
print(list(islice(agen(), 50))) # Michael S. Branicky, May 20 2025

A321537 Write n in base 10, shorten all the runs of successive identical digits by 1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 0
Offset: 0

Views

Author

N. J. A. Sloane, Nov 13 2018

Keywords

Comments

More than the usual number of terms are shown in order to reach some interesting terms.
All primes vanish except those in A050758.

Examples

			22 -> 2, so a(22)=2 is the first term > 1.
10 in not reached until a(1100) = 10.

Links

Crossrefs

A base-10 analog of A318921.
Cf. A321536, A050758.

Programs

  • Maple
    read("transforms"):
A321537 := proc(n)
    local dgsin,dgsout,pos ;
    dgsin := convert(n,base,10) ;
    dgsout := [] ;
    for pos from 2 to nops(dgsin) do
        if op(pos,dgsin) = op(pos-1,dgsin) then
            dgsout := [op(pos,dgsin),op(dgsout)] ;
        end if;
    end do:
    digcatL(dgsout) ;
end proc: # R. J. Mathar, Nov 14 2018
  • Mathematica
    Array[FromDigits[Join @@ Map[Most, Split@ IntegerDigits@ #]] &, 123] (* Michael De Vlieger, Nov 13 2018 *)
  • PARI
    a(n)={my(v=digits(n)); my(L=List()); for(i=1, #v, my(t=v[i]); if(i>1 && t==v[i-1], listput(L,t))); fromdigits(Vec(L))} \\ Andrew Howroyd, Nov 13 2018
  • Python
    from re import split
def A321537(n):
    return int('0'+''.join(d[:-1] for d in split('(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)',str(n)) if d != '' and d != None)) # Chai Wah Wu, Nov 13 2018

A384013 Primes with at least two identical leading digits.

Original entry on oeis.org

11, 113, 223, 227, 229, 331, 337, 443, 449, 557, 661, 773, 881, 883, 887, 991, 997, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 3301, 3307, 3313
Offset: 1

Views

Author

Stefano Spezia, May 17 2025

Keywords

Crossrefs

Cf. A383978, A384014, A384015.
Subsequence of A050758.
Cf. A062353 (variant).

Programs

  • Mathematica
    Select[Prime[Range[5,500]],Part[d=IntegerDigits[#],1]==Part[d,2] &]

A384015 Primes with at least two identical trailing digits and at least two identical leading digits.

Original entry on oeis.org

11, 11177, 11299, 11311, 11399, 11411, 11633, 11677, 11699, 11777, 11833, 11933, 22111, 22133, 22277, 22433, 22511, 22699, 22777, 22811, 22877, 33199, 33211, 33311, 33377, 33533, 33577, 33599, 33811, 33911, 44111, 44533, 44633, 44699, 44711, 44777, 55333, 55399
Offset: 1

Views

Author

Stefano Spezia, May 17 2025

Keywords

Crossrefs

Cf. A383978, A384013, A384016.
Subsequence of A050758.

Programs

  • Mathematica
    Select[Prime[Range[5,6000]],Part[d=IntegerDigits[#],l=IntegerLength[#]]==Part[d,l-1] && Part[d,1]==Part[d,2] &]
  • Python
    from itertools import count, islice
from sympy import isprime
def A384015_gen(): # generator of terms
    yield 11
    for n in count(2):
        yield from filter(isprime,(i+j+k for i in range(11*10**(n-2),11*10**(n-1),11*10**(n-2)) for j in range(0,10**(n-2),100) for k in (11,33,77,99)))
A384015_list = list(islice(A384015_gen(),38)) # Chai Wah Wu, May 20 2025

A050757 Primes containing no pair of consecutive equal digits.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 313, 317, 347, 349
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Crossrefs

Cf. A043096, A000040, A050758, A029743.

Programs

  • Mathematica
    t={}; Do[p = Prime[n]; If[!MemberQ[Differences[IntegerDigits[p]],0], AppendTo[t,p]], {n,70}]; t (* Jayanta Basu, May 04 2013 *)

Extensions

Offset corrected by Arkadiusz Wesolowski, Jan 12 2012

A050786 Palindromic primes containing at least one pair of consecutive equal digits.

Original entry on oeis.org

11, 11311, 11411, 13331, 15551, 16661, 19991, 33533, 72227, 75557, 76667, 77377, 77477, 77977, 78887, 79997, 1003001, 1008001, 1022201, 1055501, 1114111, 1117111, 1120211, 1123211, 1126211, 1129211, 1134311, 1145411, 1150511
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Crossrefs

Cf. A002385, A050785, A050784, A050758.

Programs

  • Mathematica
    Select[Prime[Range[89500]],Reverse[x=IntegerDigits[#]]==x&&MemberQ[Differences[x],0]&] (* Jayanta Basu, Jun 01 2013 *)

A261510 Triangle-congruent primes greater than 10 with a single digit at the center.

Original entry on oeis.org

1111211111, 1111411111, 3333133333, 9999499999, 1111111111112111111111111111, 1111311331137311333311111111, 1111411441142411444411111111, 1111611661167611666611111111, 1111811881185811888811111111, 3333033003305033000033333333, 3333133113312133111133333333
Offset: 1

Views

Author

Felix Fröhlich, Aug 22 2015

Keywords

Comments

Subsequence of A050758.

Examples

			a(6) can be represented as follows:
......1
.....1 1
....1 3 1
...1 3 3 1
..1 3 7 3 1
.1 3 3 3 3 1
1 1 1 1 1 1 1

Links

Crossrefs

Cf. A050758.
Showing 1-7 of 7 results.

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

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