A271626 -id:A271626 - cp's OEIS frontend

A271629 Squares that are the sum of the digits of the numbers from 0 to n, for some n.

0, 1, 36, 81, 100, 144, 289, 441, 784, 900, 1225, 1296, 3025, 3600, 5041, 5625, 6400, 8100, 8649, 10000, 11881, 15625, 15876, 18225, 23716, 36100, 41616, 44100, 50625, 55225, 57600, 62001, 67600, 72900, 78400, 99225, 122500, 129600, 136900, 145161, 168921, 189225

Offset: 1

Paolo P. Lava, Apr 11 2016

			0 = 0^2; 1 = 1^2; 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A037123, A271626.

with(numtheory): P:=proc(q) local a,b,c,k,n; a:=0; for n from 0 to q do b:=0; c:=n;
for k from 1 to ilog10(n)+1 do b:=b+(c mod 10); c:=trunc(c/10); od; a:=a+b;
if a=trunc(sqrt(a))*trunc(sqrt(a)) then print(a); fi; od; end: P(10^6);

Select[Accumulate@ Map[Total@ IntegerDigits@ # &, Range[0, 10^4]], IntegerQ@ Sqrt@ # &] (* Michael De Vlieger, Apr 11 2016 *)

lista(nn) = for (n=0, nn, if (issquare(s=sum(k=1, n, sumdigits(k))), print1(s, ", "))); \\ Michel Marcus, Apr 11 2016

A271628 Primes that are the sum of the digits of the numbers from 1 to n, for some n.

Original entry on oeis.org

3, 73, 109, 127, 433, 1009, 1117, 1801, 2017, 2089, 2143, 2467, 2503, 2791, 3079, 3331, 3583, 4159, 4519, 4663, 4951, 5437, 5581, 5923, 6121, 6301, 6553, 7039, 7561, 8353, 8623, 8821, 9001, 9199, 9631, 9811, 10837, 11719, 12637, 13177, 13249, 13627, 14401, 15391

Offset: 1

Paolo P. Lava, Apr 11 2016

			The sum of the digits of 1 and 2 is a prime: 1 + 2 = 3.
The sum of the digits of the number from 1 to 16 is a prime: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3 + 1 + 4 + 1 + 5 + 1 + 6 = 73.

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Cf. A000040, A037123, A271626.

with(numtheory): P:=proc(q) local a,b,c,k,n; a:=0;
for n from 0 to q do b:=0; c:=n; for k from 1 to ilog10(n)+1 do b:=b+(c mod 10); c:=trunc(c/10); od; a:=a+b;
if isprime(a) then print(a); fi; od; end: P(10^6);

Select[Accumulate@ Map[Total@ IntegerDigits@ # &, Range[0, 1200]], PrimeQ] (* Michael De Vlieger, Apr 11 2016 *)

lista(nn) = for (n=1, nn, if (isprime(p=sum(k=1, n, sumdigits(k))), print1(p, ", "))); \\ Michel Marcus, Apr 11 2016

cp's OEIS Frontend

A271629 Squares that are the sum of the digits of the numbers from 0 to n, for some n.

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