A268605 a(1) = 0; a(n+1) is the smallest integer in which the difference between its digits sum and the a(n) digits sum is equal to the n-th prime.

0, 2, 5, 19, 89, 1999, 59999, 4999999, 599999999, 199999999999, 399999999999999, 799999999999999999, 8999999999999999999999, 499999999999999999999999999, 29999999999999999999999999999999, 4999999999999999999999999999999999999

Offset: 1

Author

Francesco Di Matteo, Feb 17 2016

Keywords

• nonn
• base

Comments

First 8 terms are primes (and are also in A061248). Next terms are not always primes.

Examples

			a(4) = 19 and 1 + 9 = 10; so a(5) = 89 because 8 + 9 = 17 and 17 - 10 = 7, that is the 4th prime.
		

Links

• Francesco Di Matteo, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A269306, A061248, A067180, A051885.

Programs

PARI

findnext(x, k) = {sx = sumdigits(x); pk = prime(k); y = 1; while (sumdigits(y) - sx != pk, y++); y;}
lista(nn) = {print1(x = 0, ", "); for (k=1, nn, y = findnext(x, k); print1(y, ", "); x = y;);} \\ Michel Marcus, Feb 19 2016

Python

sumprime = 0
isPrime=lambda x: all(x % i != 0 for i in range(int(x**0.5)+1)[2:])
print(0)
for i in range(2,100):
  if isPrime(i):
    alfa = ""
    k = i + sumprime
    sumprime = k
    while k > 9:
      alfa = alfa + "9"
      k = k - 9
    alfa = str(k)+alfa
    print(alfa)

Formula

a(n) = A051885( A007504(n-1) ). - R. J. Mathar, Jun 19 2021

Extensions

NAME adapted to offset by R. J. Mathar, Jun 19 2021