A244444 Numbers n such that n+sigma(n) is a repunit number.

4, 5, 506311, 4761903, 506767303, 5517762660583, 5554746531623, 5555541480743

Offset

1,1

Comments

This sequence is a subsequence of A116017.

a(6) > 10^11. - Hiroaki Yamanouchi, Aug 26 2014

a(9) > 10^13. The numbers 47379454926624737751 and 546139199807860751551844463475591 belong to this sequence. - Giovanni Resta, Aug 17 2019

a(9) <= 5458110152757191. Also in the sequence is 38808343270779723425176258917550576371890625326889683884600092615. - Daniel Suteu, Aug 23 2019

Links

Table of n, a(n) for n=1..8.

Example

sigma(4761903)+4761903 = 11111111.

Prog

(PARI)
for(n=1, 10^10, d=digits(sigma(n)+n); if(vecmax(d)==1&&vecmin(d)==1, print1(n, ", "))) \\ Derek Orr, Aug 02 2014
(Python) from sympy import divisors
[n for n in range(1, 10**6) if len(set(str(n+sum(divisors(n))))) == 1 and str(n+sum(divisors(n)))[0] == '1'] # Chai Wah Wu, Aug 04 2014

Crossrefs

Cf. A116017, A309835.

Sequence in context: A058916 A064612 A299639 * A231407 A005927 A201529

Adjacent sequences: A244441 A244442 A244443 * A244445 A244446 A244447

Keyword

nonn,base,more,hard

Author

Farideh Firoozbakht, Aug 01 2014

Extensions

a(5) from Hiroaki Yamanouchi, Aug 26 2014

a(6)-a(8) from Giovanni Resta, Aug 17 2019

Status

approved