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.

A154729 Products of three distinct primes of the form 6*k + 1.

Original entry on oeis.org

1729, 2821, 3367, 3913, 4123, 4921, 5551, 5719, 6097, 6643, 7189, 7657, 8029, 8113, 8827, 8911, 9139, 9331, 9373, 9709, 9919, 10507, 10621, 11137, 11557, 12649, 12901, 13237, 13699, 13741, 14287, 14497, 14539, 14833, 14911, 15067, 15799, 15841
Offset: 1

Views

Author

Omar E. Pol, Jan 18 2009

Keywords

Comments

a(1) = 1729 is the Hardy-Ramanujan number (see taxicab numbers in A001235, A011541).
Equivalently, products of three distinct primes of the form 3*k + 1. - Omar E. Pol, Feb 17 2018

Examples

			The first three primes of the form 6*k + 1 are 7, 13 and 19, so a(1) = 7*13*19 = 1729. - _Omar E. Pol_, Feb 17 2018

Links

Crossrefs

Subsequence of A007304.
Cf. A001235, A002476, A011541, A154716, A154717, A154728.

Programs

  • Mathematica
    Module[{nn=40,prs},prs=Select[6*Range[nn]+1,PrimeQ];Take[Times@@@ Subsets[ prs,{3}]//Union,nn]] (* Harvey P. Dale, Feb 17 2018 *)
  • PARI
    fct(n, o=[1])=if(n>1, concat(apply(t->vector(t[2], i, t[1]), Vec(factor(n)~))), o) \\ after M. F. Hasler in A027746
is(n) = my(f=fct(n)); if(#f!=3 || f!=vecsort(f, , 8), return(0), for(k=1, #f, if((f[k]-1)/6!=ceil((f[k]-1)/6), return(0)))); 1 \\ Felix Fröhlich, Jul 07 2021

Extensions

a(5)-a(38) from Donovan Johnson, Jan 28 2009

A154728 Products of three consecutive primes of the form 6n+1 (see A002476).

Original entry on oeis.org

1729, 7657, 21793, 49321, 97051, 175741, 298351, 386389, 559399, 789289, 1089019, 1425829, 1924177, 2665603, 3295273, 3864241, 4631971, 5694079, 6951667, 8103877, 9363547, 10775137, 12307147, 14956219, 18091147, 21243961, 24066037
Offset: 1

Views

Author

Omar E. Pol, Jan 18 2009, Jan 21 2009

Keywords

Comments

Note that a(1)=1729 is the Hardy-Ramanujan number (see taxicab numbers in A001235, A011541).

Examples

			13, 19, 31 are three consecutive primes of the form 6n+1 and 13*19*31 = 7657. - _Emeric Deutsch_, Jan 21 2009

Links

Crossrefs

Cf. A001235, A002476, A011541, A154716, A154717, A154729.

Programs

  • Maple
    a := proc (n) if `mod`(ithprime(n), 6) = 1 then ithprime(n) else end if end proc: A := [seq(a(n), n = 1 .. 100)]: seq(A[j]*A[j+1]*A[j+2], j = 1 .. 30); # Emeric Deutsch, Jan 21 2009
  • Mathematica
    Times@@@Partition[Select[Prime[Range[100]],IntegerQ[(#-1)/6]&],3,1] (* Harvey P. Dale, Jan 13 2019 *)

Extensions

Extended by Emeric Deutsch, Jan 21 2009

A154716 Products of three consecutive happy primes A035497.

Original entry on oeis.org

1729, 5681, 13547, 56327, 237553, 789289, 1089019, 1560553, 2530217, 4480109, 7703209, 12131401, 18417101, 24119467, 30355679, 38022301, 46039783, 53272619, 57627329, 62188859, 79075651, 112140029, 169169677, 226833263, 271152373, 300157327, 325898231
Offset: 1

Views

Author

Omar E. Pol, Jan 18 2009

Keywords

Comments

Note that a(1) = 1729 is the Hardy-Ramanujan number (see taxicab numbers in A001235, A011541).

Crossrefs

Cf. A001235, A011541, A035497, A154717, A154728, A154729.

Programs

  • Mathematica
    happyQ[n_, b_] := NestWhile[Total[IntegerDigits[#, b]^2] &, n, UnsameQ, All] == 1; Times @@@ Partition[Select[Prime[Range[150]], happyQ[#, 10] &], 3, 1] (* Amiram Eldar, Jan 17 2025 *)

Extensions

a(5)-a(27) from Nathaniel Johnston, Apr 30 2011
Showing 1-3 of 3 results.

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