keyword:dumb - cp's OEIS frontend

A031214 Initial term of sequence An.

0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 8, 14, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 4, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1

Offset: 1

Jeff Burch

This ignores the offset and gives the first term of the actual entry.
Since the sequences in the OEIS occasionally change their initial terms (for editorial reasons), this is an especially ill-defined sequence! - N. J. A. Sloane, Jan 01 2005
Sequences like this are deprecated. - Joerg Arndt, Apr 16 2020

			A000001 begins 0,1,1,1,2,1,2,1,5,2,... so a(1) = 0 = a(31214).

PrimeFan, Esoteric Integer Sequences
PrimeFan, Esoteric Integer Sequences [Cached copy]
N. J. A. Sloane, Online Encyclopedia of Integer Sequences
Index entries for sequences whose definition involves A_n (or An).

Cf. A039928, A051070, A091967, A107357, A102288; also A000001, A000002, A000003, A000004, A000005, etc.

Data updated by Sean A. Irvine, Apr 16 2020

A326178 Number of subsets of {1..n} whose product is equal to their sum.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

Offset: 0

Gus Wiseman, Jun 13 2019

Same as A001477 (the nonnegative integers) with 3 removed.

			The a(1) = 1 through a(9) = 10 subsets:
  {1}  {1}  {1}      {1}      {1}      {1}      {1}      {1}      {1}
       {2}  {2}      {2}      {2}      {2}      {2}      {2}      {2}
            {3}      {3}      {3}      {3}      {3}      {3}      {3}
            {1,2,3}  {4}      {4}      {4}      {4}      {4}      {4}
                     {1,2,3}  {5}      {5}      {5}      {5}      {5}
                              {1,2,3}  {6}      {6}      {6}      {6}
                                       {1,2,3}  {7}      {7}      {7}
                                                {1,2,3}  {8}      {8}
                                                         {1,2,3}  {9}
                                                                  {1,2,3}

Cf. A053632, A057567, A057568, A063865, A301987, A326156, A326158, A326179, A326180.

Table[Length[Select[Subsets[Range[n]],Times@@#==Plus@@#&]],{n,0,10}]

A159911 Prime times: primes of the form HMM with primes H, MM, 0

Original entry on oeis.org

211, 223, 229, 241, 307, 311, 313, 317, 331, 337, 347, 353, 359, 503, 523, 541, 547, 719, 743, 1103, 1117, 1123, 1129, 1153, 1303, 1307, 1319, 1723, 1741, 1747, 1753, 1759, 1907, 1913, 1931, 2311, 2341, 2347

Offset: 1

M. F. Hasler, May 01 2009

Suggested by E. Angelini, cf. link.

E. Angelini, in "Les membres de ce groupe forment un nombre premier", April 30, 2009.

See also A050246 and A229106, where H and MM (and SS) do not need to be prime.

Select[Flatten[Table[FromDigits[Join[IntegerDigits[h],PadLeft[ IntegerDigits[ m],2]]],{h,Prime[Range[9]]},{m,Prime[Range[ 17]]}]],PrimeQ] (* Harvey P. Dale, Mar 27 2022 *)

forprime( h=0,24, forprime( m=0,60, isprime(100*h+m) & print1(100*h+m,", ")))

A186086 Beastly primes (version 1): either 666 followed by 0's and a 1 or 7 at the right end or a palindrome with 666 in the center, 0's surrounding these digits, and 1 or 7 at both ends.

Original entry on oeis.org

6661, 16661, 66601, 76667, 700666007, 6660000000001, 666000000000001, 700000666000007, 70000006660000007, 6660000000000000000000000007, 66600000000000000000000000007, 1000000000000066600000000000001

Offset: 1

Arkadiusz Wesolowski, Feb 12 2011

Differs from A131645 in that 26669, 46663, 56663, 66617, 66629, 66643, 66653, 66683, 66697, 96661, 96667, 106661, 106663, 106669, 116663, 146669, 166601, 166603, 166609, 166613, 166619, 166627, 166631, 166643, 166657, 166667, 166669, 166679, are not included here.

76667 is the largest beastly prime that does not contain the digit "0".

Charles R Greathouse IV, Table of n, a(n) for n = 1..33
Chris Caldwell, The Prime Glossary, Beastly prime
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6661
R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations (May 2001), p. 5
Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)
Eric Weisstein's World of Mathematics, Beast Number

Cf. A046720, A051003, A131645, A164968, A196023, A138563, A186630, A186538, A156166, A186521.

e = 14; p = 666*10^n + 1; q = (10^(n + 2) + 666)*10^n + 1; Select[Union[Table[p, {n, 2*e}], Table[p + 6, {n, 2*e}], Table[q, {n, e}], Table[q + 6*10^(2*n + 2) + 6, {n, e}]], PrimeQ] (* Arkadiusz Wesolowski, Sep 21 2011 *)
Module[{nn=35,bp1,bp2,bp3,bp4}, bp1=FromDigits/@ Table[Join[PadRight[ {6,6,6},n1,0],{1}],{n1,3,nn}]; bp2=FromDigits/@ Table[Join[ PadRight[ {6,6,6},n2,0],{7}], {n2,3,nn}]; bp3=FromDigits/@ Table[Join[PadRight[ {1},n3,0], {6,6,6},PadLeft[ {1},n3,0]],{n3,1,nn/2}];bp4=FromDigits/@ Table[Join[PadRight[{7},n3,0],{6,6,6}, PadLeft[ {7},n3,0]],{n3,1,nn/2}]; Select[Sort[Join[bp1,bp2,bp3,bp4]],PrimeQ]] (* Harvey P. Dale, Jan 18 2017 *)

Edited by N. J. A. Sloane, Feb 12 2011

a(10)-a(12) from Charles R Greathouse IV, Feb 12 2011

A019440 Integers in alphabetical order in British English.

Original entry on oeis.org

8, 8000000000000, 8000000000008, 8000000000018, 8000000000080, 8000000000088, 8000000000085

Offset: 1

N. J. A. Sloane, Neil Fernandez

			The list begins "eight", "eight billion", "eight billion and eight", ...

Cf. A004740, A026081.

A026081 Integers in reverse alphabetical order in U.S. English.

Original entry on oeis.org

0, 2202202202202, 2202202202222, 2202202202223, 2202202202226

Offset: 1

Neil Fernandez

This sequence is ill-defined from the 2nd term on. Proof: Assume that x is the term following the initial 0. Then the number x*10^(6n), for n sufficiently large, is spelled out: name(x) name(10^(6n)). This comes after name(x) in lexicographical order, and thus before x in this sequence. - M. F. Hasler, Nov 20 2009

			Zero, two trillion, two hundred and two billion, two hundred and two million, two hundred and two thousand, two hundred and two, ...

Cf. A004740, A019440.

See A127352 for another version. - N. J. A. Sloane, Dec 05 2009

A049005 Number of letters in English names for days of week.

Original entry on oeis.org

6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8, 6, 6, 7, 9, 8, 6, 8

Offset: 0

Deepak R. N (deepak_rama(AT)bigfoot.com)

Period 7, repeat [6, 6, 7, 9, 8, 6, 8]. - Joerg Arndt, Sep 20 2023

			a(0)=6 because "Sunday" has 6 letters.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

From Elmo R. Oliveira, Jul 16 2024: (Start)
G.f.: (6 + 6*x + 7*x^2 + 9*x^3 + 8*x^4 + 6*x^5 + 8*x^6)/(1-x^7).
a(n) = a(n-7) for n >= 7. (End)

Offset 0 from Michel Marcus, Aug 12 2023

A198018 Yet unseen primes occurring within the first 1,2,3,4,... digits of Pi, A000796 (ordered according to position of last, then initial digit).

Original entry on oeis.org

3, 31, 41, 5, 314159, 14159, 4159, 59, 2, 1592653, 653, 53, 141592653589, 89, 415926535897, 5926535897, 6535897, 35897, 5897, 97, 7, 358979, 58979, 79, 589793, 9265358979323, 9323, 23, 93238462643, 462643, 643, 43, 433, 41592653589793238462643383, 89793238462643383, 38462643383, 2643383, 383, 83

Offset: 1

M. F. Hasler, Oct 20 2011

Consider the first, then the first two, then the first three, ..., terms of A000796, i.e., decimal digits of Pi. Look whether the concatenation of a certain number of subsequent digits yields a prime which did not yet occur earlier (and thus necessarily involves the last of the considered digits). If so, add this prime to the sequence.

Contains A005042 as a subsequence.

			The first digit of the sequence is the prime a(1)=3.
The first two digits, "3.1", yield the prime a(2)=31.
In "3.14" there are no more primes. In "3.141" there is the prime a(3)=41.
In "3.1415" there is the prime a(4)=5.
In "3.14159" we have the primes 314159, 14159, 4159 and 59.

Cf. A198019 ("new" primes ordered w.r.t. their size instead of starting position).

Cf. A000796, A005042, A047658.

{my(PI=digits(Pi\.1^30), seen=[]); for(i=1, #PI-1, for(j=1, i, my(p=fromdigits(PI[j..i])); !isprime(p) || setsearch(seen, p) || print1(p", ") || seen=setunion(seen,[p])))} \\ edited to use current PARI syntax by Andrew Howroyd and M. F. Hasler, May 10 2021

{my(a=List()); for(m=0, precision(.)-3, my(pi=Pi\.1^m, p); for(k=0, m, !isprime(p=pi%10^(m-k+1)) && setsearch(Set(a), p) && listput(a,p))); a} \\ M. F. Hasler, May 10 2021

A001355 Mix digits of Pi and e.

Original entry on oeis.org

3, 2, 1, 7, 4, 1, 1, 8, 5, 2, 9, 8, 2, 1, 6, 8, 5, 2, 3, 8, 5, 4, 8, 5, 9, 9, 7, 0, 9, 4, 3, 5, 2, 2, 3, 3, 8, 5, 4, 3, 6, 6, 2, 0, 6, 2, 4, 8, 3, 7, 3, 4, 8, 7, 3, 1, 2, 3, 7, 5, 9, 2, 5, 6, 0, 6, 2, 2, 8, 4, 8, 9, 4, 7, 1, 7, 9, 5, 7, 7, 1, 2, 6, 4, 9, 7, 3, 0, 9, 9, 9, 3, 3, 6, 7, 9, 5, 9, 1, 9

Offset: 1

N. J. A. Sloane

			3.21741185298216852385485997... .

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
Index entries for sequences related to the number Pi

Cf. A058382.

Flatten[Transpose[{RealDigits[Pi, 10, 50][[1]], RealDigits[E, 10, 50][[1]]}]]
Riffle[RealDigits[Pi, 10, 50][[1]], RealDigits[E, 10, 50][[1]]] (* Robert G. Wilson v, Jun 23 2014 *)

A114645 The numbers 2^n-1 written in groups of three digits, with leading zeros omitted.

Original entry on oeis.org

137, 153, 163, 127, 255, 511, 102, 320, 474, 95, 819, 116, 383, 327, 676, 553, 513, 107, 126, 214, 352, 428, 710, 485, 752, 97, 151, 419, 430, 383, 886, 71, 677, 721, 533, 554, 431, 671, 88, 631, 342, 177, 272, 684, 354, 555, 368, 709, 111, 73, 741, 823, 214, 748

Offset: 1

N. J. A. Sloane, Feb 18 2006

			1,3,7,15,31,63,...

Heard over coffee at the Computers in Scientific Discovery meeting in Ghent, Feb 02 2006.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FromDigits[#] & /@ Partition[ Flatten[ IntegerDigits[ Table[ 2^n - 1, {n, 31}]]], 3] (* Robert G. Wilson v, Jun 23 2014 *)

from itertools import count, islice
def bgen(): yield from (d for n in count(1) for d in str((1 << n)-1))
def agen(): g = bgen(); yield from (int("".join(t)) for t in zip(g, g, g))
print(list(islice(agen(), 54))) # Michael S. Branicky, Dec 25 2022

More terms from Matthew Conroy, Mar 12 2006

cp's OEIS Frontend

A031214 Initial term of sequence An.

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A326178 Number of subsets of {1..n} whose product is equal to their sum.

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Mathematica

A159911 Prime times: primes of the form HMM with primes H, MM, 0

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PARI

A186086 Beastly primes (version 1): either 666 followed by 0's and a 1 or 7 at the right end or a palindrome with 666 in the center, 0's surrounding these digits, and 1 or 7 at both ends.

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A019440 Integers in alphabetical order in British English.

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A026081 Integers in reverse alphabetical order in U.S. English.

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A049005 Number of letters in English names for days of week.

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A198018 Yet unseen primes occurring within the first 1,2,3,4,... digits of Pi, A000796 (ordered according to position of last, then initial digit).

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PARI

PARI

A001355 Mix digits of Pi and e.

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