A127721 -id:A127721 - cp's OEIS frontend

A127719 Floor of square root of sum of squares of n consecutive primes.

2, 3, 6, 9, 14, 19, 25, 32, 39, 48, 57, 68, 80, 90, 102, 115, 129, 143, 158, 173, 187, 203, 220, 237, 256, 275, 294, 313, 331, 350, 372, 394, 418, 440, 465, 488, 513, 538, 564, 590, 616, 642, 670, 697, 724, 751, 780, 811, 843, 873

Offset: 1

Artur Jasinski, Jan 25 2007

nonn

Cf. A127720, A127721.

A024450 := proc(n) local i; add((ithprime(i))^2,i=1..n); end: A000196 := proc(n) floor(sqrt(n)); end: A127719 := proc(n) A000196(A024450(n)); end: for n from 1 to 30 do printf("%d, ",A127719(n)); od; # R. J. Mathar, Jan 28 2007

a = {}; k = 0; Do[k = k + (Prime[x])^2; AppendTo[a, Floor[Sqrt[k]]], {x, 1, 50}]; a

a(n) = A000196(A024450(n)). - R. J. Mathar, Jan 28 2007

A127720 Floor of square root of sum of squares of n odd consecutive primes.

Original entry on oeis.org

3, 5, 9, 14, 19, 25, 31, 39, 48, 57, 68, 80, 90, 102, 115, 129, 143, 157, 173, 187, 203, 220, 237, 256, 275, 294, 313, 331, 350, 372, 394, 418, 440, 465, 488, 513, 538, 564, 590, 616, 642, 670, 697, 724, 751, 780, 811, 843, 873

Offset: 1

Artur Jasinski, Jan 25 2007

nonn

Cf. A127719, A127721.

A024450 := proc(n) local i ; add((ithprime(i))^2,i=1..n) ; end: Ax := proc(n) A024450(n+1)-4 ; end: A000196 := proc(n) floor(sqrt(n)) ; end: A127720 := proc(n) A000196(Ax(n)) ; end: for n from 1 to 30 do printf("%d, ",A127720(n)) ; od ; # R. J. Mathar, Jan 28 2007

a = {}; k = 0; Do[k = k + (Prime[x])^2; AppendTo[a, Floor[Sqrt[k]]], {x, 2, 50}]; a
Module[{nn=50},Floor[Sqrt[#]]&/@Accumulate[Prime[Range[2,nn+1]]^2]] (* Harvey P. Dale, Jul 27 2017 *)

a(n) = A000196(A024450(n+1) - 4). - R. J. Mathar, Jan 28 2007

A127722 Floor of square root of sum of squares of n consecutive odd numbers.

Original entry on oeis.org

1, 3, 5, 9, 12, 16, 21, 26, 31, 36, 42, 47, 54, 60, 67, 73, 80, 88, 95, 103, 111, 119, 127, 135, 144, 153, 161, 171, 180, 189, 199, 208, 218, 228, 239, 249, 259, 270, 281, 292, 303, 314, 325, 336, 348, 360, 372, 383, 396, 408, 420, 432, 445, 458, 470, 483, 496

Offset: 1

Artur Jasinski, Jan 25 2007

nonn

Cf. A127719, A127720, A127721.

A000447 := proc(n) binomial(2*n+1,3) ; end: A000196 := proc(n) floor(sqrt(n)) ; end: A127722 := proc(n) A000196(A000447(n)) ; end: for n from 1 to 30 do printf("%d, ",A127722(n)) ; od ; # R. J. Mathar, Jan 28 2007

a = {}; k = 0; Do[k = k + x^2; AppendTo[a, Floor[Sqrt[k]]], {x, 1, 150, 2}]; a

a(n) = A000196[A000447(n)]. - R. J. Mathar, Jan 28 2007

A127723 Floor of square root of sum of squares of the first n consecutive even numbers.

Original entry on oeis.org

2, 4, 7, 10, 14, 19, 23, 28, 33, 39, 44, 50, 57, 63, 70, 77, 84, 91, 99, 107, 115, 123, 131, 140, 148, 157, 166, 175, 184, 194, 204, 213, 223, 233, 244, 254, 265, 275, 286, 297, 308, 319, 331, 342, 354, 366, 377, 389, 402, 414, 426, 439, 451, 464, 477, 490, 503

Offset: 1

Artur Jasinski, Jan 25 2007

nonn

Cf. A127719, A127720, A127721, A127722.

a = {}; k = 0; Do[k = k + x^2; AppendTo[a, Floor[Sqrt[k]]], {x, 2, 150, 2}]; a
Floor[Sqrt[#]]&/@Accumulate[Range[2,120,2]^2] (* Harvey P. Dale, Nov 04 2012 *)

Definition clarified by Harvey P. Dale, Nov 04 2012

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A127719 Floor of square root of sum of squares of n consecutive primes.

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A127720 Floor of square root of sum of squares of n odd consecutive primes.

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A127722 Floor of square root of sum of squares of n consecutive odd numbers.

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A127723 Floor of square root of sum of squares of the first n consecutive even numbers.

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