A094830 -id:A094830 - cp's OEIS frontend

A094877 Primes that are reached in A094830.

2, 2, 3, 199, 5, 107, 7, 547, 263, 11, 11, 17, 13, 31, 41, 53, 17, 83, 19, 199, 643, 563, 23, 199, 547, 643, 1301, 227, 29, 563, 31, 643, 439, 59, 643, 199, 37, 199, 563, 269, 41, 107, 43, 199, 643, 643, 47, 197, 199, 149, 439, 199, 53, 547, 131, 269, 131, 227, 59

Offset: 1

Jason Earls, Jun 15 2004

If n is prime, a(n) = n. - Robert Israel, Oct 27 2016

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

Cf. A094830.

f:= proc(n) local x, t;
  x:= n;
  do
   if isprime(x) then return x fi;
   x:= x + add(t^2, t = convert(x,base,10))
  od;
end proc:
map(f, [$1..100]); # Robert Israel, Oct 27 2016

p2[n_]:=NestWhile[#+Total[IntegerDigits[#]^2]&,n,!PrimeQ[#]&]; Array[p2,60] (* Harvey P. Dale, Dec 03 2011 *)

A094878 n sets a new record in A094830.

Original entry on oeis.org

1, 4, 8, 21, 27, 64, 253, 1629, 4284, 4416, 5992, 19621, 78399, 204347, 298735, 848999, 1202402, 1496888, 1539370, 1987614, 2859485, 5460483, 6160282, 14539187, 22103424, 40412450, 95261053, 105703913, 105703932, 123434487

Offset: 1

Jason Earls, Jun 15 2004

nonn

a(15)-a(30) from Donovan Johnson, Feb 06 2010

A094879 Where 1's occur in A094830 (nonprimes that reach a prime in one step under iteration of "x -> x + sum of squares of digits of x").

Original entry on oeis.org

1, 10, 12, 14, 15, 16, 18, 34, 57, 74, 75, 78, 91, 94, 100, 102, 105, 108, 121, 122, 123, 126, 128, 140, 142, 146, 148, 160, 161, 165, 166, 168, 182, 183, 188, 213, 216, 217, 234, 275, 297, 301, 324, 327, 341, 387, 412, 413, 415, 418, 432, 450, 453, 455, 458

Offset: 1

Jason Earls, Jun 15 2004

Select[Range[500],!PrimeQ[#]&&PrimeQ[#+Total[IntegerDigits[#]^2]]&] (* Harvey P. Dale, Mar 15 2015 *)

A277717 Primes that only occur once in A094877.

Original entry on oeis.org

3, 5, 7, 13, 19, 23, 29, 37, 43, 47, 61, 67, 71, 73, 79, 89, 97, 103, 109, 113, 151, 179, 181, 193, 211, 223, 233, 241, 277, 281, 283, 293, 307, 313, 331, 337, 347, 349, 359, 373, 379, 383, 397, 401, 409, 419, 421, 443, 449, 463, 467, 479, 487, 523, 557

Offset: 1

Robert Israel, Oct 27 2016

Primes n that are not k + A003132(k) for any nonprime k < n.

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

Cf. A003132, A094830, A094877.

N:= 1000: # to get the first N terms
res:= NULL: count := 0:
for n from 1 while count < N do
  if isprime(n) then
    if R[n] <> false then count:= count+1; res:= res, n fi
  else
    v:= n + add(t^2, t=convert(n,base,10));
    if isprime(v) then R[v]:= false fi;
  fi
od:
res;

With[{nn = 1200}, TakeWhile[#, # <= nn/2 &] &@ First@ Transpose@ TakeWhile[#, Last@ # == 1 &] &@ SortBy[#, Last] &@ Tally@ Array[NestWhile[# + Total[IntegerDigits[#]^2] &, #, ! PrimeQ@ # &] &, nn]] (* Michael De Vlieger, Oct 27 2016, after Harvey P. Dale at A094877 *)

cp's OEIS Frontend

A094877 Primes that are reached in A094830.

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A094878 n sets a new record in A094830.

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A094879 Where 1's occur in A094830 (nonprimes that reach a prime in one step under iteration of "x -> x + sum of squares of digits of x").

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Mathematica

A277717 Primes that only occur once in A094877.

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Programs

Maple

Mathematica