A076161 -id:A076161 - 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

A033936 a(n+1) = a(n) + sum of squares of digits of a(n).

Original entry on oeis.org

1, 2, 6, 42, 62, 102, 107, 157, 232, 249, 350, 384, 473, 547, 637, 731, 790, 920, 1005, 1031, 1042, 1063, 1109, 1192, 1279, 1414, 1448, 1545, 1612, 1654, 1732, 1795, 1951, 2059, 2169, 2291, 2381, 2459, 2585, 2703, 2765, 2879, 3077, 3184

Offset: 0

Olivier Gorin (gorin(AT)roazhon.inra.fr)

Orbit of 1 under iterations of A258881. - M. F. Hasler, Jul 23 2015

			After 1063, since 1^2 + 0^2 + 6^2 + 3^2 = 46 we get 1063+46 = 1109.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A258881, A003132, A076161.

A[0] := 1;
for n to 50 do
   A[n] := A[n-1]+add(t^2, t = convert(A[n-1], base, 10))
od:
seq(A[i],i=0..50); # Robert Israel, Feb 15 2018

NestList[#+Total[IntegerDigits[#]^2]&,1,45] (* Harvey P. Dale, Aug 14 2011 *)

a(n+1) = A258881(a(n)). a(n) = (A258881^n)(1). - M. F. Hasler, Jul 23 2015

A259567 Number of subsequent numbers, starting with n, for which A258881(x) = x + (sum of squares of digits of x) is prime.

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 0

M. F. Hasler, Jul 19 2015

This sequence is motivated by sequence A259391 and the "Prime puzzle 776".

			For n = 0, A258881(0) = 0 is not prime.
For n = 1, A258881(1) = 1+1 = 2 is prime, but A258881(2) = 2+4 is not prime, therefore a(1)=1.
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, but A258881(20) = 20 + 2^2 + 0^2 is not prime, therefore a(10) = 10.
The next value of 10 occurs at index n = 1761702690, see A259391.

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

Cf. A259391, A258881, A003132, A076161, A033936.

a(n)=for(m=n,n+9e9,isprime(A258881(m))||return(m-n))

If a(n) > 0, then a(n+1) = a(n)-1.

a(n) > 0 iff n is in A076161.

cp's OEIS Frontend

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

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A033936 a(n+1) = a(n) + sum of squares of digits of a(n).

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A259567 Number of subsequent numbers, starting with n, for which A258881(x) = x + (sum of squares of digits of x) is prime.

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