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 1-3 of 3 results.

A090712 Primes whose base-13 expansion is a (valid) decimal expansion of a prime.

Original entry on oeis.org

2, 3, 5, 7, 29, 53, 59, 79, 107, 113, 241, 263, 269, 293, 367, 373, 419, 443, 521, 523, 547, 601, 607, 631, 677, 757, 761, 787, 937, 971, 1021, 1069, 1093, 1231, 1249, 1277, 1307, 1361, 1381, 1433, 1459, 1543, 1567, 1613, 1619, 2213, 2237, 2239, 2447, 2477
Offset: 1

Views

Author

Cino Hilliard, Jan 18 2004

Keywords

Comments

See A235110 for a similar sequence whose definition works "in the opposite direction": Actually, the base-13 representation of the terms here. - M. F. Hasler, Jan 03 2014

Examples

			The prime p = 53 is written 41 in base 13, and 41 is again (the base 10 representation of) a prime. Therefore p = 53 is a term of this sequence. [Rephrased by _M. F. Hasler_, Jan 03 2014]

Links

Crossrefs

Cf. A090707 - A091924.

Programs

  • Mathematica
    f[n_]:=Module[{c13=FromDigits[IntegerDigits[n],13]},If[PrimeQ[c13], c13,0]]; Select[f/@Prime[Range[500]],#!=0&] (* Harvey P. Dale, Jun 20 2011 *)
  • PARI
    is_A090712(p)=vecmax(d=digits(p,13))<10&&isprime(vector(#d,i,10^(#d-i))*d~)&&isprime(p) \\ M. F. Hasler, Jan 05 2014

Extensions

Edited by N. J. A. Sloane, Feb 07 2007, and by M. F. Hasler, Jan 05 2014

A235126 Primes whose base-10 representation also represents a prime in base 17.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 43, 61, 67, 83, 137, 139, 191, 197, 227, 241, 263, 313, 331, 461, 577, 593, 599, 607, 683, 739, 821, 863, 937, 953, 1013, 1033, 1039, 1051, 1297, 1303, 1327, 1459, 1619, 1693, 1721, 1787, 1811, 1877, 1949
Offset: 1

Views

Author

M. F. Hasler, Jan 03 2014

Keywords

Comments

See A090713 for a similar sequence whose definition works "in the opposite direction".

Examples

			The decimal representation of prime 23, considered as a number written in base 17, stands for 2*17+3 = 37, which is also prime, therefore 23 is in the sequence.

Links

Crossrefs

Cf. A235110 and other sequences in the range A090707 - A091924.

Programs

  • Maple
    filter:= proc(p) local L;
  if not isprime(p) then return false fi;
  L:= convert(p,base,10);
  isprime(add(L[i]*17^(i-1),i=1..nops(L)))
end proc:
select(filter, [2,seq(i,i=3..10000,2)]); # Robert Israel, Apr 25 2017
  • Mathematica
    Select[Prime@ Range@ 300, PrimeQ@ FromDigits[IntegerDigits@ #, 17] &] (* Michael De Vlieger, Jan 03 2016 *)
  • PARI
    is(p, b=17)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows the production of similar sequences for other bases b > 9 (which can be given as an optional 2nd argument), but does not do the required check for bases b < 10.

A235144 Primes whose base-10 representation also represents a prime in base 19.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 43, 47, 113, 131, 151, 157, 179, 199, 229, 263, 283, 311, 317, 353, 359, 409, 421, 443, 461, 557, 593, 641, 661, 739, 773, 809, 821, 881, 937, 953, 977, 1031, 1109, 1213, 1217, 1231, 1279, 1291, 1297, 1307, 1433, 1439, 1583, 1657, 1693, 1697, 1741, 1789, 1811, 1873, 1877, 1949, 1987, 2003
Offset: 1

Views

Author

M. F. Hasler, Jan 03 2014

Keywords

Comments

See A090714 for a similar sequence whose definition works "in the opposite direction".

Examples

			The decimal representation of prime 23, considered as a number written in base 19, stands for 2*19 + 3 = 41, which is also prime, therefore 23 is in the sequence.

Links

Crossrefs

Cf. A235110, A235126 and other sequences in the range A090707 - A091924.

Programs

  • Mathematica
    Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#], 19]] &] (* Alonso del Arte, Jan 04 2014 *)
  • PARI
    is_A235144(p, b=19)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows one to produce similar sequences for other bases b > 9 (which can be given as optional 2nd argument), but does not do the required check for bases b < 10.
Showing 1-3 of 3 results.

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

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