A259567 -id:A259567 - cp's OEIS frontend

A258881 a(n) = n + the sum of the squared digits of n.

0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 11, 13, 17, 23, 31, 41, 53, 67, 83, 101, 24, 26, 30, 36, 44, 54, 66, 80, 96, 114, 39, 41, 45, 51, 59, 69, 81, 95, 111, 129, 56, 58, 62, 68, 76, 86, 98, 112, 128, 146, 75, 77, 81, 87, 95, 105, 117, 131, 147, 165, 96, 98, 102

Offset: 0

M. F. Hasler, Jul 19 2015

Carlos Rivera, Puzzle 776. Ten consecutive integers such that..., The Prime Puzzles and Problems Connection, March 2015.

Cf. A003132, A062028, A259391, A259567, A033936, A076161 (indices of primes), A329179 (indices of squares).

Total[Flatten@ {#, IntegerDigits[#]^2}] & /@ Range[0, 61] (* Michael De Vlieger, Jul 20 2015 *)
Table[n+Total[IntegerDigits[n]^2],{n,0,100}] (* Harvey P. Dale, Nov 27 2022 *)

PARI
```
A258881(n)=n+norml2(digits(n))
```

def ssd(n): return sum(int(d)**2 for d in str(n))
def a(n): return n + ssd(n)
print([a(n) for n in range(63)]) # Michael S. Branicky, Jan 30 2021

A076161 Numbers n such that n + sum of squares of digits of n (A258881) is a prime.

Original entry on oeis.org

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 31, 34, 57, 73, 74, 75, 78, 91, 94, 97, 100, 101, 102, 103, 105, 107, 108, 109, 121, 122, 123, 126, 127, 128, 140, 142, 146, 148, 160, 161, 165, 166, 168, 182, 183, 188, 213, 216, 217, 234, 251, 275, 277, 297, 301

Offset: 1

Zak Seidov, Nov 01 2002

			12 is a term because 12+(1^2+2^2) = 17 is a prime.

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

Cf. A258881, A259391, A259567.

filter:= proc(n) local t; isprime(n+add(t^2,t=convert(n,base,10))) end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 30 2021

isok(n) = isprime(n + norml2(digits(n))); \\ Michel Marcus, Jan 31 2021

from sympy import isprime
def ssd(n): return sum(int(d)**2 for d in str(n))
def ok(n): return isprime(n + ssd(n))
def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]
print(aupto(301)) # Michael S. Branicky, Jan 30 2021

A259391 Numbers n such that A258881(n+k) is prime for k=0,...,9; where A258881(x) = x + sum of the square of the digits of x (A003132).

Original entry on oeis.org

10, 1761702690, 7226006660, 16453361570, 95748657190, 104217487100, 111058349320, 141665059420, 168759510430, 177313689280, 177313689330, 178209124090, 188343072120, 347296044930, 347296045010, 381449093790, 381449093840, 445151776780, 491570264380

Offset: 1

M. F. Hasler, Jul 19 2015

Terms computed by G. Resta, cf. link to Prime Puzzle 776.

			For n = 10, A258881(10) = 10 + 1^2 + 0^2 = 11, A258881(11) = 11 + 1^2 + 1^2 = 13, A258881(12) = 12 + 1^2 + 2^2 = 17, ..., A258881(19) = 19 + 1^2 + 9^2 = 101 are all prime, therefore a(1) = 10.
The next value of 10 in A259567 occurs at index n = 1761702690 = a(2).

C. Riviera, Puzzle 776. Ten consecutive integers such that..., PrimePuzzles.net, March 2015.

Cf. A003132, A258881, A259567.

cp's OEIS Frontend

A258881 a(n) = n + the sum of the squared digits of n.

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A076161 Numbers n such that n + sum of squares of digits of n (A258881) is a prime.

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Programs

Maple

PARI

Python

A259391 Numbers n such that A258881(n+k) is prime for k=0,...,9; where A258881(x) = x + sum of the square of the digits of x (A003132).

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