A052196 -id:A052196 - cp's OEIS frontend

A080777 a(n), when spelled in English, is the smallest positive integer with exactly n letters.

1, 4, 3, 11, 15, 13, 17, 24, 23, 73, 101, 104, 103, 111, 115, 113, 117, 124, 123, 173, 323, 373, 1104, 1103, 1111, 1115, 1113, 1117, 1124, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373

Offset: 3

Peter Kolbus (peter(AT)kolbusfamily.com), Mar 11 2003

In this version 101 is written "one hundred one", etc.

This uses the conventions that "and" is never used and two-digit numbers are not used before "hundred". The sequence is labeled "finite" because there is no widely accepted naming convention for arbitrarily large numbers. - David Wasserman, Dec 20 2004

			The 3rd term has 5 letters; the smallest positive integer with this number of letters is 3 (three).

Hans Havermann, Table of n, a(n) for n = 3..758
Hans Havermann, Growth illustration for this sequence

Cf. A001166, A052196 (the 'largest' analog of this sequence), A084390.

(* Works for a(n) up to 10^k *)
k=5;name[n_]:=IntegerName[n,"Words"];
nameLen[n_]:=StringLength[StringReplace[name[n],{" "-> "","-"-> "",","-> ""}]];
max[n_]:=Max[nameLen/@Range[10^(n-1)+1,10^n]];max10toK=max/@Range[k];
pos[n_Integer/;n>2]:=Position[Sort[Append[max10toK,n]],n,1][[1,1]]-1;
a[n_Integer/;n>2&&n<(10^k)+1]:=Module[{l=10^pos[n]},While[nameLen[l]!=n,l++];l];
a/@Range[3,40] (* Ivan N. Ianakiev, Sep 05 2018 *)

Corrected by James Ong (blackshadowshade(AT)yahoo.com.au), Jun 27 2003
More terms from Brian Galebach, Feb 06 2004
Edited by David Wasserman, Dec 20 2004

A052187 a(n) is the smallest prime p such that p, p+d, and p+2d are consecutive primes where d = 2 for n = 1 and d = 6*(n-1) for n > 1.

Original entry on oeis.org

3, 47, 199, 20183, 16763, 69593, 255767, 247099, 3565931, 6314393, 4911251, 12012677, 23346737, 43607351, 34346203, 36598517, 51041957, 460475467, 652576321, 742585183, 530324329, 807620651, 2988119207, 12447231761, 383204539, 4470607951, 5007182707

Offset: 1

Labos Elemer, Jan 28 2000

nonn

The first term 3 is anomalous since for all others d is divisible by 6. These are minimal terms if in A047948 d=6 is replaced by possible differences: (2), 6, 12, 18, ..., 54, 60.

a(54) > 5*10^13, while a(55) = 46186474937633. - Giovanni Resta, Apr 08 2013

			a(2)=47 and it is the lower border of a dd pattern: 47[6 ]53[6 ]59. a(10)=6314393 and a(10)+54=6314447, a(10)+108=6314501 are consecutive primes and 6314393 is the smallest prime prior to a (54,54) difference pattern of A001223.

Jerry M Lagrou, Table of n, a(n) for n = 1..72 (terms 1..39 from Donovan Johnson, terms 40..53 from Giovanni Resta)

Cf. A001223, A047948, A052160, A054342.

Cf. A052188, A052189, A052195, A052196, A052197, A052198.

a = Table[0, {100}]; NextPrime[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = q = r = 0; Do[r = NextPrime[r]; If[r + p == 2q && r - q < 201 && a[[(r - q)/2]] == 0, a[[(r - q)/2]] = p]; p = q; q = r, {n, 1, 10^6}]; a (* Typos fixed by Zak Seidov, May 01 2020 *)

list(n)=ve=vector(n);ppp=2;pp=3;forprime(p=5,,d=p-pp;if(pp-ppp==d,i=d\6+1;if(i<=n&&ve[i]==0,ve[i]=ppp;print1(".");vecprod(ve)>0&&return(ve)));ppp=pp;pp=p) \\ Jeppe Stig Nielsen, Apr 17 2022

The least prime(k) such that prime(k+1) = (prime(k) + prime(k+2))/2 and prime(k+1) - prime(k) = d is either 2 or divisible by 6.

a(1) = A054342(1) - 2. For n>1, a(n) = A054342(n) - 6*(n-1). - Jeppe Stig Nielsen, Apr 16 2022

More terms from Labos Elemer, Jan 04 2002
More terms from Robert G. Wilson v, Jan 06 2002
Definition clarified by Harvey P. Dale, Aug 29 2012
a(23)-a(27) from Donovan Johnson, Aug 30 2012
Name edited by Jon E. Schoenfield, Nov 30 2023

cp's OEIS Frontend

A080777 a(n), when spelled in English, is the smallest positive integer with exactly n letters.

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