login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321024 Let j be one of the prime factors of k. Sequence lists numbers k such that the prime before j is a prime factor of k+1. 1
3, 5, 9, 14, 15, 20, 21, 27, 33, 35, 39, 45, 49, 50, 51, 55, 57, 63, 65, 69, 75, 80, 81, 84, 87, 93, 95, 99, 105, 110, 111, 117, 119, 123, 125, 129, 132, 135, 140, 141, 147, 152, 153, 154, 155, 159, 165, 170, 171, 177, 183, 185, 189, 195, 200, 201, 207, 208, 209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Contains arbitrarily long strings of consecutive integers. Here are the shortest ones arranged by increasing numbers of terms:

{3}

{14,15}

{49,50,51}

{152,153,154,155}

{10217,10218,10219,10220,10221}

{634842, 634843, 634844, 634845, 634846, 634847}

{123945, 123946, 123947, 123948, 123949, 123950, 123951}

{2852055, 2852056, 2852057, 2852058, 2852059, 2852060, 2852061, 2852062}

{49057063, 49057064, 49057065, 49057066, 49057067, 49057068, 49057069, 49057070, 49057071}, etc.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..5000

EXAMPLE

152 is divisible by 19 and 153 by 17;

153 is divisible by 3 and 154 by 2;

154 is divisible by 7 and 155 by 5;

155 is divisible by 5 and 156 by 3.

MAPLE

with(numtheory): P:=proc(n) local a, k;

a:=factorset(n) minus {2};

for k from 1 to nops(a) do if frac((n+1)/prevprime(a[k]))=0

then RETURN(n); fi; od; end: seq(P(i), i=2..300);

MATHEMATICA

Select[Range[210], Function[k, AnyTrue[DeleteCases[NextPrime[ FactorInteger[k][[All, 1]], -1 ], p_ /; p < 0], Mod[k + 1, #] == 0 &]]] (* Michael De Vlieger, Oct 31 2018 *)

PROG

(PARI) is(n) = my(f = factor(n>>valuation(n, 2))[, 1]); n++; for(i = 1, #f~, if(n % precprime(f[i]-1) == 0, return(1))); 0 \\ David A. Corneth, Oct 30 2018

CROSSREFS

Cf. A072562, A073606.

Sequence in context: A306833 A146433 A134672 * A211389 A335193 A288259

Adjacent sequences:  A321021 A321022 A321023 * A321025 A321026 A321027

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 26 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 24 20:34 EST 2020. Contains 338616 sequences. (Running on oeis4.)