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

1,2

Comments

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

Links

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

Formula

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

Example

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

Prog

(Python)
sumprime = 0
isPrime=lambda x: all(x % i != 0 for i in range(int(x**0.5)+1)[2:])
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
(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

Crossrefs

Cf. A269306, A061248, A067180, A051885.

Sequence in context: A316700 A124348 A323389 * A205804 A052324 A020115

Adjacent sequences: A268602 A268603 A268604 * A268606 A268607 A268608

Keyword

nonn,base

Author

Francesco Di Matteo, Feb 17 2016

Extensions

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

Status

approved