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 1-5 of 5 results.

A073606 Smaller of two consecutive integers divisible respectively by two consecutive primes.

Original entry on oeis.org

2, 8, 9, 14, 20, 21, 24, 26, 32, 38, 39, 44, 50, 54, 55, 56, 62, 68, 69, 74, 77, 80, 84, 86, 90, 92, 98, 99, 104, 110, 114, 115, 116, 122, 125, 128, 129, 134, 140, 144, 146, 152, 158, 159, 160, 164, 169, 170, 174, 175, 176, 182, 188, 189, 194, 195, 200, 204, 206
Offset: 1

Views

Author

Amarnath Murthy, Aug 04 2002

Keywords

Comments

There are arbitrarily long strings of consecutive integers in this sequence; for example, A072562(k+1) is followed by at least k-1 more consecutive members. - David Wasserman, Oct 21 2004

Examples

			54 is a term as 54 and 55 are divisible by 3 and 5 respectively. 55 is also a term as 55 and 56 are divisible by 5 and 7. 56 is also a term as 56 and 57 are divisible by 2 and 3.
		

Crossrefs

Programs

  • Mathematica
    f[n_Integer] := Flatten[ Table[ #1] & @@@ FactorInteger[n]]; NextPrim[n_] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[n + i, {i, 0, 1} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 1 ]]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 220} ]
    npQ[n_] := Or @@ Divisible[n + 1, NextPrime[First /@ FactorInteger[n]]]; Select[Range[2, 210], npQ[#] &] (* Jayanta Basu, Jul 03 2013 *)

Extensions

Edited by Robert G. Wilson v, Aug 07 2002

A073607 Smallest of three consecutive integers divisible by three consecutive primes respectively.

Original entry on oeis.org

8, 20, 38, 54, 68, 98, 114, 128, 158, 159, 169, 188, 218, 248, 264, 278, 308, 338, 368, 369, 398, 405, 428, 458, 474, 488, 518, 548, 578, 579, 608, 638, 668, 684, 698, 728, 758, 788, 789, 790, 791, 818, 848, 878, 894, 908, 938, 968, 998, 999, 1028, 1058
Offset: 1

Views

Author

Amarnath Murthy, Aug 04 2002

Keywords

Comments

The sequence is infinite as 30*k + 8 is a member for all k. What is the longest string of consecutive integers?

Examples

			20 is a term as 20,21 and 22 are divisible by 5,7 and 11 respectively.
114 is a term as 114, 115 and 116 are divisible by 19, 23 and 29 respectively.
		

Crossrefs

Programs

  • Mathematica
    f[ n_Integer ] := Flatten[ Table[ #1 ] & @@@ FactorInteger[ n ]]; NextPrim[ n_ ] := Block[ {k = n + 1}, While[ !PrimeQ[ k ], k++ ]; k ]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[ n + i, {i, 0, 2} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 2 ] ]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 1117} ]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Aug 06 2002

A072555 Smallest of four consecutive integers divisible by four consecutive primes respectively.

Original entry on oeis.org

158, 368, 578, 788, 789, 790, 998, 1208, 1418, 1628, 1838, 1944, 2048, 2258, 2468, 2678, 2888, 3098, 3099, 3308, 3518, 3728, 3938, 4148, 4254, 4358, 4367, 4568, 4778, 4988, 5198, 5408, 5409, 5618, 5795, 5828, 6038, 6248, 6458, 6564, 6668, 6797, 6878
Offset: 1

Views

Author

Robert G. Wilson v, Aug 06 2002

Keywords

Examples

			158 is a term as 158, 159, 160 and 161 are divisible by 2, 3, 5 and 7 respectively.
		

Crossrefs

Programs

  • Mathematica
    f[ n_Integer ] := Flatten[ Table[ #1 ] & @@@ FactorInteger[ n ] ]; NextPrim[ n_ ] := Block[ {k = n + 1}, While[ !PrimeQ[ k ], k++ ]; k ]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[ n + i, {i, 0, 3} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[ [ k ] ], 3 ] ] ] != {0}, k++ ]; If[ k < l + 1, Print[ n ] ], {n, 2, 7297} ]

A072730 Smallest of 5 consecutive integers divisible respectively by 5 consecutive primes.

Original entry on oeis.org

788, 789, 3098, 5408, 7718, 10028, 12338, 14648, 15804, 16958, 19268, 21578, 23888, 26198, 28508, 30818, 30819, 33128, 35438, 37748, 40058, 40830, 42368, 44678, 45834, 46988, 49298, 51608, 53918, 56228, 58538, 60848, 60849, 63158
Offset: 1

Views

Author

Robert G. Wilson v, Aug 07 2002

Keywords

Examples

			3098 is a term as 3098, 3099, 3100, 3101 and 3102 are divisible by 2, 3, 5, 7 and 11 respectively.
		

Crossrefs

Programs

  • Mathematica
    f[n_Integer] := Flatten[ Table[ #1] & @@@ FactorInteger[n]]; NextPrim[n_] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[n + i, {i, 0, 4} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 4 ]]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 72397} ]
    cicpQ[n_]:=Module[{num=Range[n,n+4],pr=PrimePi[n+4]-4},Total [Boole[ AllTrue[ #, IntegerQ]&/@Table[num/Prime[Range[k,k+4]],{k,pr}]]]>0]; Select[ Range[ 64000],cicpQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 11 2019 *)

A072760 Smallest of 7 consecutive integers divisible respectively by 7 consecutive primes.

Original entry on oeis.org

210998, 466254, 721508, 1232018, 1742528, 2253038, 2763548, 3274058, 3784568, 4295078, 4805588, 5316098, 5316099, 5826608, 6337118, 6847628, 7358138, 7868648, 8379158, 8889668, 9400178, 9910688, 10165944, 10421198, 10931708
Offset: 1

Views

Author

Robert G. Wilson v, Aug 08 2002

Keywords

Examples

			210998 is a term as 210998, 210999, 211000, 211001, 211002, 211003 and 211004 are divisible by 2, 3, 5, 7, 11, 13 and 17 respectively.
		

Crossrefs

Programs

  • Mathematica
    f[n_Integer] := Flatten[ Table[ #1] & @@@ FactorInteger[n]]; NextPrim[n_] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[n + i, {i, 0, 6} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 6 ]]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 811597} ]
Showing 1-5 of 5 results.