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