A171613 -id:A171613 - cp's OEIS frontend

A171615 Numbers n with property that (n^2 + sum of the digits of n^2) is odd.

4, 6, 10, 11, 12, 13, 16, 18, 19, 23, 26, 27, 28, 30, 31, 32, 33, 34, 35, 38, 40, 41, 43, 44, 48, 50, 52, 55, 56, 57, 59, 60, 62, 64, 69, 70, 71, 75, 76, 81, 82, 85, 86, 90, 94, 95, 97, 98, 99, 100, 101, 102, 103, 106, 114, 116, 118, 120, 121, 122, 123, 126, 129, 131, 135

Offset: 1

Zak Seidov, Dec 13 2009

Or, n's such that A171613(n) is odd.

Cf. A062028, A171613, A171615.

Drop[Union@Table[If[OddQ[n^2+Total[IntegerDigits[n^2]]],n,0],{n,0,200}],1]
Select[Range[150],OddQ[#^2+Total[IntegerDigits[#^2]]]&] (* Harvey P. Dale, Feb 18 2015 *)

A209303 Numbers of the form x^2 + SumOfSquaredDigits(x).

Original entry on oeis.org

2, 8, 18, 32, 50, 72, 98, 101, 123, 128, 149, 162, 179, 213, 251, 293, 339, 389, 404, 443, 446, 492, 542, 596, 654, 716, 782, 852, 909, 926, 971, 1037, 1107, 1181, 1259, 1341, 1427, 1517, 1611, 1616, 1698, 1784, 1874, 1968, 2066, 2168, 2274, 2384, 2498, 2525

Offset: 1

Christian N. K. Anderson, Apr 22 2013

Note that early terms are not always produced in order. For example, 162 is produced by x=9, but is the 12th term in the sequence. The last out-of-order term is a(30)=926, produced when x=29.

			251 is in the sequence, because 15^2 + (1^2 + 5^2) = 251.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Ulam Spiral of terms 1 to 500.

Cf. A171613, A062028, A007770.

Table[n^2+Total[IntegerDigits[n]^2],{n,100}]//Union (* Harvey P. Dale, Jan 25 2021 *)

sort((1:10000)^2+vapply(1:10000,sum(as.numeric(unlist(strsplit(as.character(as.bigz(x)),split="")))^2),1))

A171614 Numbers n with property that (n^2 + sum of the digits of n^2) is even.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 8, 9, 14, 15, 17, 20, 21, 22, 24, 25, 29, 36, 37, 39, 42, 45, 46, 47, 49, 51, 53, 54, 58, 61, 63, 65, 66, 67, 68, 72, 73, 74, 77, 78, 79, 80, 83, 84, 87, 88, 89, 91, 92, 93, 96, 104, 105, 107, 108, 109, 110, 111, 112, 113, 115, 117, 119, 124, 125, 127, 128

Offset: 1

Zak Seidov, Dec 13 2009

Or, n's such that A171613(n) is even.

Cf. A062028, A171613, A171615.

Union@Table[If[EvenQ[n^2+Total[IntegerDigits[n^2]]],n,0],{n,0,200}]
Select[Range[0,200],EvenQ[#^2+Total[IntegerDigits[#^2]]]&] (* Harvey P. Dale, Apr 01 2019 *)

A224966 Numbers n such that n^2+sum-of-digits(n^2) is prime.

Original entry on oeis.org

1, 4, 10, 16, 31, 32, 40, 41, 43, 62, 71, 76, 94, 95, 97, 98, 121, 142, 158, 163, 164, 166, 179, 188, 208, 211, 214, 227, 229, 259, 260, 265, 284, 301, 313, 317, 320, 328, 331, 340, 352, 355, 356, 365, 380, 382, 386, 392, 397, 401, 418, 424, 425, 431, 436, 439

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Apr 21 2013

This is the sequence of indices of prime numbers in A171613.

The Ulam spiral for this sequence is a near-perfect line y=-x (see links).

			a(12)=76 because 76^2=5776, and 5776+(5+7+7+6)=5801, which is prime.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, The Ulam Spiral for the prime numbers derived from this sequence, i.e. a(n)^2+sum of digits(a(n)^2)

Cf. A048521.
Cf. numbers of the form n^2+sum-of-digits(n^2) A171613, and subsets A171614, A171615.
Cf. A062028.

library(gmp); digsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split=""))))
ans=as.bigz(rep(0,100)); n=1; i=as.bigz(1)
while(n<=100) {
if(isprime((w=i^2+digsum(i^2)))) ans[(n=n+1)-1]=i
i=i+1
}; ans

cp's OEIS Frontend

A171615 Numbers n with property that (n^2 + sum of the digits of n^2) is odd.

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A209303 Numbers of the form x^2 + SumOfSquaredDigits(x).

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A171614 Numbers n with property that (n^2 + sum of the digits of n^2) is even.

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A224966 Numbers n such that n^2+sum-of-digits(n^2) is prime.

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