A171615 -id:A171615 - cp's OEIS frontend

A171613 a(n) = n^2 + sum of the digits of n^2.

0, 2, 8, 18, 23, 32, 45, 62, 74, 90, 101, 125, 153, 185, 212, 234, 269, 308, 333, 371, 404, 450, 500, 545, 594, 638, 695, 747, 803, 854, 909, 977, 1031, 1107, 1169, 1235, 1314, 1388, 1457, 1530, 1607, 1697, 1782, 1871, 1955, 2034, 2126, 2222, 2313, 2408, 2507

Offset: 0

Zak Seidov, Dec 13 2009

Subsequence of A062028 (n + sum of the digits of n).

Cf. A062028, A171614, A171615.

Table[n^2+Total[IntegerDigits[n^2]],{n,0,100}]

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

A171613 a(n) = n^2 + sum of the digits of n^2.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

R