cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A072394 Numbers n such that sigma(n)=reversal(n)-n.

Original entry on oeis.org

1563, 1633, 18673, 32207, 1405313, 1567563, 1656833, 193613415, 325933027, 376491249, 2287850446, 2432416646, 13823276223, 14055445313, 19087920283, 23804849568, 36303512827, 148868530953
Offset: 1

Views

Author

Joseph L. Pe, Jul 21 2002

Keywords

Comments

If (58*1000^n-169)/111 is prime then (58*1000^n-169)/37 is in the sequence (the proof is easy). Next term is greater than 12*10^8. - Farideh Firoozbakht, Jan 29 2006
From Farideh Firoozbakht, May 25 2010: (Start)
If p = 156/101*(10^(4n)-1)-1 is prime then 91*p is in the sequence (the proof is easy).
A178321 gives numbers n such that (58*1000^n-169)/111 = 58/111*(10^(3n)-1)-1 is prime and A178322 gives numbers n such that 156/101*(10^(4n)-1)-1 is prime. (End)
a(19) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			reverse(1563) - 1563 = 3651 - 1563 = 2088 = sigma(1563), so 1563 is a term of the sequence.
376491249 is in the sequence because sigma(376491249)=565703424 =942194673-376491249=reversal(376491249)-376491249.

Crossrefs

Cf. A072234.
Cf. A178321, A178322. [From Farideh Firoozbakht, May 25 2010]

Programs

  • Mathematica
    Select[Range[10^6], FromDigits[Reverse[IntegerDigits[n]]] - # == DivisorSigma[1, # ] &]
Do[If[DivisorSigma[1,n]==FromDigits[Reverse[IntegerDigits[n]]]- n,Print[n]],{n,1200000000}] (* Farideh Firoozbakht *)

Extensions

More terms from Farideh Firoozbakht, Jan 29 2006
a(11)-a(17) from Donovan Johnson, Dec 21 2008
a(18) from Giovanni Resta, Oct 28 2012

A178321 Numbers k such that 58/111*(10^(3*k)-1)-1 is prime.

Original entry on oeis.org

1, 2, 15, 74, 278, 541, 668, 1320, 1780, 1874, 4824, 13310, 20420, 24887
Offset: 1

Views

Author

Farideh Firoozbakht, May 26 2010

Keywords

Comments

If k is in the sequence then m=3*(58/111*(10^(3*k)-1)-1) is a term of A072394.
Namely if k is a term of this sequence then for m=1/37*(58*10^(3*k)-169) we have sigma(m)=reversal(m)-m (see comment lines of A072394).
There is no further term up to 3000. Numbers corresponding to the larger terms are probable primes.
a(15) > 50000. - Robert Price, Oct 20 2014

Crossrefs

Cf. A072394, A178322.

Programs

  • Mathematica
    Do[If[PrimeQ[58/111*(10^(3 n) - 1) - 1], Print[n]], {n, 1874}]

Extensions

a(11)-a(14) from Robert Price, Oct 20 2014
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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