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.

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A235479 Primes whose base-2 representation also is the base-9 representation of a prime.

Original entry on oeis.org

11, 13, 19, 41, 79, 109, 137, 151, 167, 191, 193, 199, 227, 239, 271, 307, 313, 421, 431, 433, 457, 487, 491, 521, 563, 613, 617, 659, 677, 709, 727, 757, 929, 947, 1009, 1033, 1051, 1249, 1483, 1693, 1697, 1709, 1721, 1831, 1951, 1979, 1987, 1993
Offset: 1

Views

Author

M. F. Hasler, Jan 12 2014

Keywords

Comments

This sequence is part of a two-dimensional array of sequences, given in the LINK, based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.
For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
A subsequence of A027697, A050150, A062090 and A176620.

Examples

			11 = 1011_2 and 1011_9 = 6571 are both prime, so 11 is a term.

Links

Crossrefs

Cf. A235466 ⊂ A077723, A235266, A152079, A235475 - A235478, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.

Programs

  • PARI
    is(p,b=9)=isprime(vector(#d=binary(p),i,b^(#d-i))*d~)&&isprime(p)

A235465 Primes whose base-8 representation also is the base-2 representation of a prime.

Original entry on oeis.org

73, 521, 577, 4673, 32833, 33289, 33353, 36929, 37441, 262153, 262217, 262657, 295433, 2097673, 2101313, 2359369, 2363401, 2392073, 16777289, 16810049, 16814089, 16814153, 16814657, 17039881, 17043977, 17076809, 18874433, 18907201, 19137089, 19140617, 134222401, 134483969, 134484481, 134513161
Offset: 1

Views

Author

M. F. Hasler, Jan 11 2014

Keywords

Comments

This sequence is part of the two-dimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.
For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=8, thus a subsequence of A077722.

Examples

			73 = 111_8 and 111_2 = 7 are both prime, so 73 is a term.

Links

Crossrefs

Cf. A235478, A235479, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Programs

  • PARI
    is(p,b=2,c=8)=vecmax(d=digits(p,c))
  • PARI
    forprime(p=1,1e3,is(p,8,2)&&print1(vector(#d=digits(p,2),i,8^(#d-i))*d~,",")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(.,2,8)
Showing 1-2 of 2 results.

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