A090862 -id:A090862 - cp's OEIS frontend

A091924 Primes such that their decimal representations interpreted in base 11 are also prime.

2, 3, 5, 7, 29, 43, 61, 67, 89, 139, 193, 197, 199, 227, 263, 269, 281, 331, 353, 373, 379, 467, 571, 601, 607, 643, 733, 797, 809, 821, 827, 887, 919, 937, 1033, 1039, 1093, 1129, 1231, 1237, 1259, 1277, 1303, 1327, 1381, 1451, 1453, 1459, 1583

Offset: 1

Reinhard Zumkeller, Feb 13 2004

See A090711 for a similar sequence whose definition works "in the opposite direction". - M. F. Hasler, Jan 03 2014

			A000040(10)=29 in base 11 is 2*11^1+9*11^0=31 prime, therefore 29 is a term.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A091923.

[n:n in PrimesUpTo(1600)| IsPrime(Seqint(Intseq(n),11))]; // Marius A. Burtea, Jun 30 2019

filter:= proc(n) local L;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  isprime(add(L[i]*11^(i-1),i=1..nops(L)))
end proc:
select(filter, [2, seq(i,i=3..10000,2)]); # Robert Israel, Jan 28 2018

Select[Prime@ Range@ 250, PrimeQ@ FromDigits[IntegerDigits@ #, 11] &] (* Michael De Vlieger, Aug 29 2015 *)

is(p,b=11)={my(d=digits(p));isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)} \\ M. F. Hasler, Jan 03 2014

A090862(A049084(a(n))) > 11 for n>4.

Corrected by Zak Seidov, Feb 25 2004

A091923 Primes whose decimal representations interpreted in base 11 are not prime.

Original entry on oeis.org

11, 13, 17, 19, 23, 31, 37, 41, 47, 53, 59, 71, 73, 79, 83, 97, 101, 103, 107, 109, 113, 127, 131, 137, 149, 151, 157, 163, 167, 173, 179, 181, 191, 211, 223, 229, 233, 239, 241, 251, 257, 271, 277, 283, 293, 307, 311, 313, 317, 337, 347, 349, 359, 367, 383

Offset: 1

Reinhard Zumkeller, Feb 13 2004

A090862(A049084(a(n))) = 11.

			A000040(9)=23 in base 11 is 2*11^1 + 3*11^0 = 25 = 5^2, therefore 29 is a term.

Marius A. Burtea, Table of n, a(n) for n = 1..1045

Cf. A091924.

[n:n in PrimesUpTo(400)| not IsPrime(Seqint(Intseq(n), 11))]; // Marius A. Burtea, Jun 30 2019

Select[Prime@Range@80, ! PrimeQ@FromDigits[IntegerDigits@#, 11] &] (* Vincenzo Librandi, Jul 01 2019 *)

isok(p) = isprime(p) && (d=digits(p)) && !isprime(fromdigits(d, 11)); \\ Michel Marcus, Jun 30 2019

Corrected by Zak Seidov, Feb 25 2004

A091922 Smallest m such that the decimal representation of the m-th prime interpreted in base n is not a prime, but prime in bases 10 <= b < n.

Original entry on oeis.org

5, 10, 19, 18, 3801, 6167, 251529, 128019, 13780180, 20576

Offset: 11

Reinhard Zumkeller, Feb 13 2004

No more terms <= 3*10^10. - Michael S. Branicky, Apr 02 2025

Cf. A090862.

f[p_] := Module[{d = IntegerDigits[p], b = 11}, While[PrimeQ[FromDigits[d, b]], b++]; b]; a[n_] := Module[{p = 11, m = 5}, While[f[p] != n, p = NextPrime[p]; m++]; m]; Array[a, 8, 11] (* Amiram Eldar, Mar 28 2025 *)

A090862(a(n)) = n and A090862(m) <> n for m < a(n).

a(17)-a(20) from Amiram Eldar, Mar 28 2025

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A091924 Primes such that their decimal representations interpreted in base 11 are also prime.

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A091923 Primes whose decimal representations interpreted in base 11 are not prime.

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Magma

Mathematica

PARI

Extensions

A091922 Smallest m such that the decimal representation of the m-th prime interpreted in base n is not a prime, but prime in bases 10 <= b < n.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions