A105981 -id:A105981 - cp's OEIS frontend

A088281 a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '1's.

11, 101, 131, 151, 181, 191, 11311, 11411, 1114111, 1117111, 111181111, 111191111, 1111118111111, 111111151111111, 111111181111111, 111111111161111111111, 11111111111111611111111111111, 111111111111111111131111111111111111111, 11111111111111111111111111911111111111111111111111111

Offset: 0

Amarnath Murthy, Sep 29 2003

For n > 1, near-repunit palindromic primes (or, palindromic terms of A105992). - Lekraj Beedassy, Jun 05 2009

Harvey P. Dale, Table of n, a(n) for n = 0..32
Index to OEIS entries related to primes involving repdigits.

Cf. A088282, A088283, A088284 (analog with string of '3's, '7's resp. '9's).
Cf. A105992 (near-repunit primes), A065074 (which contain the digit 0), A034093 (number of primes by changing one 1 to 0), A065083 (least k for which that = n).
Cf. A164937 (near-repdigit primes); with 2, ..., 9 as repeated digit: A105982, A105981, A105980, A105979, A105978, A105977, A105976, A105975.

Join[{11},Select[Flatten[Table[FromDigits[Join[PadRight[{},n,1],{d},PadRight[{},n,1]]],{n,26},{d,Cases[Range[0,9],Except[1]]}]],PrimeQ]] (* Harvey P. Dale, Nov 04 2024 *)

print1(11); for(L=1,19,for(d=0,9,d!=1 && ispseudoprime(p=10^(2*L+1)\9+(d-1)*10^L) && print1(","p))) \\ M. F. Hasler, Feb 07 2020

More terms from David Wasserman, Aug 03 2005
Offset changed from 0 to 1 by Lekraj Beedassy, Jun 05 2009
Edited by M. F. Hasler, Feb 07 2020

A164937 Near-repdigit primes.

Original entry on oeis.org

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, 877, 881, 883, 887, 911, 919, 929, 977, 991, 997, 1117, 1151, 1171, 1181, 1511

Offset: 1

G. L. Honaker, Jr., Aug 31 2009

Robert G. Wilson v, Table of n, a(n) for n = 1..22172 (first 5000 terms from Arkadiusz Wesolowski)
Chris Caldwell, The Top 20 Near-repdigit Primes
Chris Caldwell, The Prime Glossary, Near-repdigit prime
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015)

Cf. A105992, A105975, A105976, A105977, A105978, A105979, A105980, A105981, A105982, A065074.

lst = {}; Do[If[PrimeQ[n] && SortBy[Tally[IntegerDigits[n]], Last][[-1, -1]] == IntegerLength[n] - 1, AppendTo[lst, n]], {n, 101, 10^3}]; lst (* Arkadiusz Wesolowski, Sep 18 2011 *)
lst = {}; Do[r = (10^n - 1)/9; Do[AppendTo[lst, DeleteCases[Select[FromDigits[Permutations[Append[IntegerDigits[a*r], d]]], PrimeQ], r | 2 | 3 | 5 | 7]], {a, 9}, {d, 0, 9}], {n, 2, 6}]; Sort[Flatten[lst]] (* Arkadiusz Wesolowski, Sep 22 2011 *)

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    for d in count(3):
        ds = set()
        for end in "1379":
            ds.update(int(c*(d-1) + end) for c in "123456789" if c != end)
            for diff in "0123456789":
                if end == diff: continue
                cands = (end*i + diff + end*(d-1-i) for i in range(d-1))
                ds.update(int(t) for t in cands if t[0] != "0")
        yield from sorted(t for t in ds if isprime(t))
print(list(islice(agen(), 52))) # Michael S. Branicky, May 17 2022

Three more terms from Lekraj Beedassy, Dec 06 2009

A168439 Near-repdigit primes with 3 as the repeated digit, and either 2 or 4 as the single digit in base 10.

Original entry on oeis.org

23, 43, 233, 433, 2333, 3323, 3343, 3433, 23333, 33343, 323333, 333233, 333323, 333433, 334333, 343333, 3233333, 3333233, 3333433, 3433333, 32333333, 33323333, 34333333, 333233333, 333334333, 3233333333, 3333323333, 3333332333, 3333333323, 3334333333, 23333333333, 33333333343, 333332333333, 333333333323, 333333343333, 3333333333433, 3433333333333, 33332333333333, 33333233333333, 33333333332333, 33333333333323, 33333333433333

Offset: 1

Lekraj Beedassy, Nov 25 2009

Union of A168438 and A138974.

Harvey P. Dale, Table of n, a(n) for n = 1..1608 (All terms having 401 or fewer digits)

Cf. A105981, A137248, A138975, A168438, A138974.

(* First run the programs for A168438 and A138974 *) Take[Union[A168438, A138974], 40]
Select[Flatten[Table[FromDigits/@Permutations[Join[{m},PadRight[{},n,3]]],{n,14},{m,{2,4}}]],PrimeQ]//Sort (* Harvey P. Dale, Oct 08 2018 *)

a(1)-a(28) verified and a(29)-a(42) added by Alonso del Arte, Dec 15 2009

A178001 Largest n-digit prime with the most digits equal to 3.

Original entry on oeis.org

3, 83, 733, 7333, 38333, 733333, 3733333, 83333333, 373333333, 3334333333, 38333333333, 383333333333, 3433333333333, 53333333333333, 383333333333333, 3733333333333333, 43333333333333333, 353333333333333333

Offset: 1

Lekraj Beedassy, May 17 2010

Select first for the most 3's, then take the largest.

Cf. A037059, A105981

cp's OEIS Frontend

A088281 a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '1's.

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A164937 Near-repdigit primes.

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A168439 Near-repdigit primes with 3 as the repeated digit, and either 2 or 4 as the single digit in base 10.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A178001 Largest n-digit prime with the most digits equal to 3.

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Author

Keywords

Comments

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