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.

Previous Showing 51-56 of 56 results.

A386325 Primes without {0, 7} as digits.

Original entry on oeis.org

2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 59, 61, 83, 89, 113, 131, 139, 149, 151, 163, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 251, 263, 269, 281, 283, 293, 311, 313, 331, 349, 353, 359, 383, 389, 419, 421, 431, 433, 439, 443, 449, 461, 463, 491
Offset: 1

Views

Author

Jason Bard, Jul 19 2025

Keywords

Links

Crossrefs

Intersection of A038615 and A038618.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 3, 4, 5, 6, 8, 9]];
  • Mathematica
    Select[Prime[Range[120]], DigitCount[#, 10, 0] == 0 && DigitCount[#, 10, 7] == 0 &]
  • PARI
    primes_with(, 1, [1, 2, 3, 4, 5, 6, 8, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("12345689"), 41))) # uses function/imports in A385776

A386326 Primes without {0, 8} as digits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 293, 311, 313, 317, 331, 337
Offset: 1

Views

Author

Jason Bard, Jul 19 2025

Keywords

Links

Crossrefs

Intersection of A038616 and A038618.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 3, 4, 5, 6, 7, 9]];
  • Mathematica
    Select[Prime[Range[120]], DigitCount[#, 10, 0] == 0 && DigitCount[#, 10, 8] == 0 &]
  • PARI
    primes_with(, 1, [1, 2, 3, 4, 5, 6, 7, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("12345679"), 41))) # uses function/imports in A385776

A386327 Primes without {0, 9} as digits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 113, 127, 131, 137, 151, 157, 163, 167, 173, 181, 211, 223, 227, 233, 241, 251, 257, 263, 271, 277, 281, 283, 311, 313, 317, 331, 337, 347, 353, 367, 373, 383, 421, 431, 433, 443, 457, 461
Offset: 1

Views

Author

Jason Bard, Jul 19 2025

Keywords

Links

Crossrefs

Intersection of A038617 and A038618.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 3, 4, 5, 6, 7, 8]];
  • Mathematica
    Select[Prime[Range[120]], DigitCount[#, 10, 0] == 0 && DigitCount[#, 10, 9] == 0 &]
  • PARI
    primes_with(, 1, [1, 2, 3, 4, 5, 6, 7, 8]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("12345678"), 41))) # uses function/imports in A385776

A103548 a(n) is the largest n-digit zeroless prime such that the sum of the two numbers that result from splitting a(n) between any two of its digits is a distinct prime.

Original entry on oeis.org

89, 863, 8821, 68683, 864883, 6866683
Offset: 2

Views

Author

Ray G. Opao, Mar 23 2005

Keywords

Comments

There is no such 8-digit prime, i.e., the sequence ends at a(7) -- although in theory a(n) might exist for some n > 8. - Hagen von Eitzen, Jun 02 2009
A term must have the last digit coprime to 10 (odd and not divisible by 5), the others from {2, 4, 6, 8}. - David A. Corneth, Aug 28 2023

Examples

			a(4) = 8821:
  8 + 821 = 829, which is prime;
  88 + 21 = 109, which is prime;
  882 + 1 = 883, which is prime;
and no larger 4-digit number has this property.

Crossrefs

Cf. A038618.

Programs

  • PARI
    a(n) = {my(lds = [9,7,3,1], s = (10^n\9-1)*10); forvec(x = vector(n-1,i,[1,4]), b = s - 20*fromdigits(Vec(x)); for(j = 1, #lds, if(iscan(b + lds[j]), return(b + lds[j])))); -1}
  • PARI
    iscan(n) = {if(n%3 == 0, return(0)); if(!isprime(n), return(0)); my(l = List(), lp, rp, qd = #digits(n-1)); for(i = 1, qd, rp = n % 10^i; lp = n \ 10^i; if(!isprime(rp + lp), return(0), listput(l, rp + lp))); #Set(l) == qd} \\ David A. Corneth, Aug 28 2023

Extensions

Last terms a(6) and a(7) from Hagen von Eitzen, Jun 02 2009

A155833 Primes in which smallest digit is final digit.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 41, 43, 53, 61, 71, 73, 83, 97, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 353, 373, 383, 421, 431, 433, 443, 461, 463, 491, 521, 541, 563, 571, 593, 631, 641, 643, 653, 661, 673, 683, 691, 733, 743, 751, 761, 773, 787, 797, 811
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 28 2009

Keywords

Comments

The final digit does not have to be the only smallest digit, so 211 is a term even though the second digit as well as the last digit equals 1. - Harvey P. Dale, Jul 21 2020

Crossrefs

Subsequence of A038618.

Programs

  • Maple
    A010879 := proc(n) n mod 10 ; end: A054054 := proc(n) min(op(convert(n,base,10))) ; end: for i from 1 to 500 do p := ithprime(i) ; if A010879(p) = A054054(p) then printf("%d,",p) ; fi; od: # R. J. Mathar, Jan 31 2009
  • Mathematica
    Select[Prime[Range[150]],Min[IntegerDigits[#]]==IntegerDigits[#][[-1]]&] (* Harvey P. Dale, Jul 21 2020 *)
  • PARI
    is(n)=my(d=digits(n));d[#d]==vecsort(d)[1] && isprime(n) \\ Charles R Greathouse IV, Dec 29 2012

Extensions

Corrected by R. J. Mathar, Jan 31 2009

A385056 Prime numbers whose digit product is a positive cube.

Original entry on oeis.org

11, 139, 181, 193, 241, 389, 421, 811, 839, 881, 983, 1181, 1193, 1319, 1777, 1811, 1913, 1931, 1999, 2141, 2221, 2269, 2411, 2663, 3119, 3191, 3313, 3331, 3463, 3643, 3833, 3889, 3911, 4211, 4363, 4441, 4691, 6229, 6263, 6343, 6491, 6661, 7177, 7717, 7877, 8111
Offset: 1

Views

Author

Mohd Anwar Jamal Faiz, Jun 16 2025

Keywords

Crossrefs

Intersection of A000040 and A237767.
Subsequence of A038618.
Cf. A184328.

Programs

  • Maple
    q:= n-> isprime(n) and (p-> p>0 and iroot(p, 3)^3=p)(mul(i, i=convert(n, base, 10))):
select(q, [$2..10000])[];  # Alois P. Heinz, Jun 16 2025
  • Mathematica
    q[n_] := Module[{pd = Times @@ IntegerDigits[n]}, pd > 0 && IntegerQ[Surd[pd, 3]]]; Select[Prime[Range[1300]], q] (* Amiram Eldar, Jun 16 2025 *)
  • PARI
    isok(k) = if (isprime(k), my(p=vecprod(digits(k))); p && ispower(p, 3)); \\ Michel Marcus, Jun 16 2025
  • Python
    from sympy import primerange, integer_nthroot
from math import prod
is_cube = lambda n: n > 0 and integer_nthroot(n, 3)[1]
digit_product = lambda n: prod(map(int, str(n)))
cubigit_primes = [p for p in primerange(2, 100000) if is_cube(dp := digit_product(p))]
print(cubigit_primes)
Previous Showing 51-56 of 56 results.

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