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.

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

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