A090092 -id:A090092 - cp's OEIS frontend

A090093 a(n) is the smallest composite number coprime to n, n+1, n+2, n+3.

25, 49, 49, 121, 121, 25, 121, 49, 49, 49, 25, 121, 121, 121, 49, 25, 49, 121, 169, 169, 25, 49, 49, 49, 121, 25, 121, 121, 49, 49, 25, 169, 169, 121, 121, 25, 49, 49, 121, 121, 25, 169, 49, 49, 49, 25, 121, 121, 121, 49, 25, 49, 169, 169, 169, 25, 49, 49, 49, 121, 25

Offset: 1

Labos Elemer, Nov 26 2003

nonn

Cf. A053669, A053670, A053671, A053672, A053673, A053674.

Cf. A090092, A090094, A090095.

m=0;Table[fla=1;Do[s=GCD[n, k];s1=GCD[n, k+1]; s2=GCD[n, k+2];s3=GCD[n, k+3];If[Equal[s, 1]&&Equal[s1, 1] &&Equal[s2, 1]&&Equal[s3, 1]&&!PrimeQ[n]&&!Equal[n, 1] &&Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 1000}], {k, 1, 256}]
With[{compnos=Complement[Range[2,500],Prime[Range[PrimePi[500]]]]}, Table[ First[Select[compnos,And@@CoprimeQ[#,n+Range[0,3]]&]],{n,70}]] (* Harvey P. Dale, Aug 10 2011 *)

a(n) = A053672(n)^2.

A090095 a(n) is the smallest composite number coprime to n, n+1, n+2, n+3, n+4 and n+5.

Original entry on oeis.org

49, 121, 121, 121, 121, 169, 169, 49, 289, 289, 289, 121, 121, 121, 49, 121, 169, 169, 169, 169, 289, 49, 121, 121, 121, 121, 121, 169, 49, 169, 169, 169, 169, 121, 121, 49, 121, 121, 289, 169, 169, 169, 49, 169, 121, 121, 121, 121, 121, 49, 361, 289, 169, 169

Offset: 1

Labos Elemer, Nov 26 2003

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A053669, A053670, A053671, A053672, A053673, A053674.

Cf. A090092, A090093, A090094.

m=0;Table[fla=1;Do[s=GCD[n, k];s1=GCD[n, k+1]; s2=GCD[n, k+2];s3=GCD[n, k+3];s4=GCD[n, k+4];s5=GCD[n, k+5]; If[Equal[s, 1]&&Equal[s1, 1]&&Equal[s2, 1]&&Equal[s3, 1]&& Equal[s4, 1]&&Equal[s5, 1]&&!PrimeQ[n]&&!Equal[n, 1]&&Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 1000}], {k, 1, 256}]
scn[n_]:=Module[{k=4,c=n+Range[0,5]},While[PrimeQ[k]||!AllTrue[c,CoprimeQ[ k,#]&],k++];k]; Array[scn,60] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 30 2020 *)

a(n) = A053674(n)^2.

A090094 a(n) is the smallest composite number coprime to n, n+1, n+2, n+3 and n+4.

Original entry on oeis.org

49, 49, 121, 121, 121, 121, 169, 49, 49, 289, 289, 121, 121, 121, 49, 49, 121, 169, 169, 169, 169, 49, 49, 121, 121, 121, 121, 121, 49, 49, 169, 169, 169, 121, 121, 49, 49, 121, 121, 169, 169, 169, 49, 49, 121, 121, 121, 121, 121, 49, 49, 289, 169, 169, 169, 121, 49

Offset: 1

Labos Elemer, Nov 26 2003

nonn

Cf. A053669, A053670, A053671, A053672, A053673, A053674.

Cf. A090092, A090093, A090095.

m=0;Table[fla=1;Do[s=GCD[n, k];s1=GCD[n, k+1]; s2=GCD[n, k+2];s3=GCD[n, k+3];s4=GCD[n, k+4];s5=GCD[n, k+5]; If[Equal[s, 1]&&Equal[s1, 1]&&Equal[s2, 1]&&Equal[s3, 1]&& Equal[s4, 1]&&!PrimeQ[n]&&!Equal[n, 1]&&Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 1000}], {k, 1, 256}]
scn[n_]:=Module[{cn=4},While[!CompositeQ[cn]||!And@@CoprimeQ[ Range[ n,n+4], cn], cn++]; cn]; Array[scn,60] (* Harvey P. Dale, Aug 12 2014 *)

a(n) = A053673(n)^2.

A089091 a(n) is the smallest composite number coprime to n and n+1.

Original entry on oeis.org

9, 25, 25, 9, 49, 25, 9, 25, 49, 9, 25, 25, 9, 121, 49, 9, 25, 25, 9, 121, 25, 9, 25, 49, 9, 25, 25, 9, 49, 49, 9, 25, 25, 9, 121, 25, 9, 25, 49, 9, 25, 25, 9, 49, 49, 9, 25, 25, 9, 49, 25, 9, 25, 49, 9, 25, 25, 9, 49, 49, 9, 25, 25, 9, 49, 25, 9, 25, 121, 9, 25, 25, 9, 49, 49, 9, 25, 25

Offset: 1

Labos Elemer, Nov 26 2003

Cf. A007978, A053669, A053670, A053671, A053672, A053673, A053674.

Cf. A090092, A090093.

m=0;Table[fla=1;Do[s=GCD[n, k]; s1=GCD[n, k+1];s2=GCD[n, k+2];s3=GCD[n, k+3]; If[Equal[s, 1]&&Equal[s1, 1]&&!PrimeQ[n]&&!Equal[n, 1]&& Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 1000}], {k, 1, 256}]

from math import gcd
def a(n):
    k, m = 3, n*(n+1)
    while gcd(k, m) != 1: k += 2
    return k*k
print([a(n) for n in range(1, 79)]) # Michael S. Branicky, Sep 25 2021

a(n) = A053670(n)^2.

Offset corrected by Mohammed Yaseen, Aug 15 2023

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A090093 a(n) is the smallest composite number coprime to n, n+1, n+2, n+3.

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A090095 a(n) is the smallest composite number coprime to n, n+1, n+2, n+3, n+4 and n+5.

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A090094 a(n) is the smallest composite number coprime to n, n+1, n+2, n+3 and n+4.

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A089091 a(n) is the smallest composite number coprime to n and n+1.

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