A250715 -id:A250715 - cp's OEIS frontend

A250482 Numbers of the form 2^x + y^2, with x and y >=0.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 20, 24, 25, 26, 27, 29, 32, 33, 36, 37, 38, 40, 41, 44, 48, 50, 51, 52, 53, 57, 64, 65, 66, 68, 72, 73, 80, 81, 82, 83, 85, 89, 96, 97, 100, 101, 102, 104, 108, 113, 116, 122, 123, 125, 128, 129, 132, 137, 144

Offset: 1

Vincenzo Librandi, Nov 24 2014

nonn

No terms are congruent to 7 mod 8: subsequence of A004777.

			12 is in this sequence because 2^3+2^2 = 12.
51 is in this sequence because 2^1+7^2 = 51.

Vincenzo Librandi, Table of n, a(n) for n = 1..2500

Cf. A004777, A250481.

Cf. sequences of the type k^x+y^k: this sequence (k=2), A250483 (k=3), A250545 (k=4), A250546 (k=5), A250547 (k=6), A250715 (k=7).

nn=15; Union[Select[Flatten[Table[2^x + y^2, {x, 0, nn}, {y, 0, nn}]], # <=nn^2 &]]

isok(n) = {k=0; while (2^k <= n, if (issquare(n - 2^k), return(1)); k++;); return (0);} \\ Michel Marcus, Nov 24 2014

A250844 Primes of the form 7^x + y^7 with x, y > 0.

Original entry on oeis.org

16433, 33191, 134033, 6044737, 40633543, 50353607, 268435463, 268437857, 268452263, 274200257, 1977343127, 2245762199, 2494358231, 4471684631, 4586471767, 13841567137, 21870016807, 21870117649, 52523350487, 54500676887, 78364166497, 92205451297, 97157445863

Offset: 1

Vincenzo Librandi, Dec 01 2014

nonn

Conjecture: a(n+1)>=a(n)+42, with equality for infinitely many n,

namely those of the form a(n)=7^1+y^7, a(n+1)=7^2+y^7. - Robert Israel, May 09 2018

			16433 is in this sequence because 16433 is prime and 7^2+3^7 = 16433.
33191 is in this sequence because 33191 is prime and 7^5+4^7 = 33191.

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

Cf. A250715.

Cf. similar sequences listed in A250481.

N:= 10^12: # to get all terms <= N
sort(select(isprime, [seq(seq(7^x+y^7, y=2..floor((N-7^x)^(1/7)),2),x=1..floor(log[7](N)))])); # Robert Israel, May 09 2018

f[x_, y_]:= 7^x + y^7; lst={}; Do[p=f[x, y]; If[PrimeQ[p], AppendTo[lst, p]], {y, 50}, {x, 50}]; Take[Union[lst], 30]
With[{nn=40},Take[Sort[Select[7^#[[1]]+#[[2]]^7&/@Tuples[Range[nn],2], PrimeQ]],nn]] (* Harvey P. Dale, May 28 2015 *)

cp's OEIS Frontend

A250482 Numbers of the form 2^x + y^2, with x and y >=0.

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