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.

A270231 Smaller member of a twin prime pair with a perfect power sum.

Original entry on oeis.org

3, 17, 71, 107, 881, 1151, 2591, 3527, 4049, 15137, 20807, 34847, 46817, 69191, 83231, 103967, 112337, 139967, 149057, 176417, 179999, 206081, 281249, 362951, 388961, 438047, 472391, 478241, 538721, 649799, 734471, 808991, 960497, 1080449, 1143071, 1152161, 1254527
Offset: 1

Views

Author

Altug Alkan, Mar 13 2016

Keywords

Comments

A069496 is a subsequence.

Examples

			3 is a term because 3 + 5 = 2^3.
17 is a term because 17 + 19 = 6^2.
107 is a term because 107 + 109 = 6^3.
139967 is a term because 139967 + 139969 = 6^7.

Links

Crossrefs

Cf. A001359, A069496, A330978, A330980.
First bisection of A119768.

Programs

  • Magma
    [p:p in PrimesUpTo(1300000)|IsPrime(p+2) and IsPower(2*p+2)]; // Marius A. Burtea, Dec 20 2019
  • PARI
    t(n,p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
for(n=1, 1e4, if(ispower(2*t(n)+2), print1(t(n), ", ")));

A330978 a(n) = (p1 + p2)/36 such that p1 >= 5 and p2 = p1 + 2 are twin primes and p1 + p2 is a k-th power with k > 1.

Original entry on oeis.org

1, 4, 6, 49, 64, 144, 196, 225, 841, 1156, 1936, 2601, 3844, 4624, 5776, 6241, 7776, 8281, 9801, 10000, 11449, 15625, 20164, 21609, 24336, 26244, 26569, 29929, 36100, 40804, 44944, 53361, 60025, 63504, 64009, 69696, 87025, 93636, 100489, 108900, 109561, 126025
Offset: 1

Views

Author

Hugo Pfoertner, Jan 05 2020

Keywords

Examples

			a(1) = 1: p1 = 17 and p2 = 19 are the first such pair, with p1 + p2 = 36 = 6^2, (17 + 19)/36 = 1;
a(2) = 4: p1 = 71, p2 = 73; p1 + p2 = 144 = 12^2, (71 + 73)/36 = 4.

Links

Crossrefs

Cf. A119768, A270231, A330980.

Programs

  • Maple
    isa := n -> isprime(n) and isprime(n+2) and iperfpow(2*n+2) <> FAIL:
select(isa, [$4..1000000]): map(n -> (n+1)/18, %); # Peter Luschny, Jan 05 2020
  • PARI
    my(pp=5); forprime(p=7,130000, if(p-pp==2, if(ispower(p+pp), print1((p+pp)/36,", "))); pp=p)

A330980 a(n) = (p1 + p2)/216 such that p1 >= 5 and p2 = p1 + 2 are twin primes and p1 + p2 is a k-th power with k >= 3.

Original entry on oeis.org

1, 1296, 24389, 274625, 531441, 970299, 2343750, 2515456, 4492125, 5268024, 5451776, 6967871, 8000000, 18821096, 25672375, 27270901, 32461759, 37748736, 41421736, 43243551, 50653000, 64000000, 69426531, 80062991, 81746504, 82881856, 94818816, 100663296
Offset: 1

Views

Author

Hugo Pfoertner, Jan 05 2020

Keywords

Comments

The values of k corresponding to the first terms are: 3, 7, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, ...

Examples

			a(1) = 1: p1 = 107 and p2 = 109 is the first pair with a sum that is a 3rd power, 216=6^3;
a(2) = 1296: p1 = 1296*108 - 1 = 139967, p2 = 1296*108 + 1 = 139969, p1 + p2 = 279936 = 6^7.

Links

Crossrefs

Cf. A076467, A119768, A270231, A330978.

Programs

  • PARI
    my(pp=5,j); forprime(p=7,10000000000, if(p-pp==2, if(j=ispower(p+pp), if(j>2, print1((p+pp)/216,", ")))); pp=p)
Showing 1-3 of 3 results.

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

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