A154703 -id:A154703 - cp's OEIS frontend

A191233 The number of times that the n-th digit of A154703(n) occurs in A154703(n).

1, 1, 5, 8, 11, 4, 16, 19, 23, 27, 32, 14, 38, 42, 47, 51, 23, 61, 64, 31, 35, 37, 80, 84, 47, 50, 96, 101, 106, 59, 117, 120, 123, 127, 131, 136, 83, 145, 150, 155, 160, 165, 172, 175, 109, 112, 189, 116, 201, 206, 125, 218, 129, 130, 232, 236, 147, 245, 156

Offset: 1

Juri-Stepan Gerasimov, May 27 2011

			A154703(3) = 1011101. The third digit of 1011101 is "1", which occurs 5 times in 1011101. Thus a(3) = 5.
A154703(4) = 1011101111. The fourth digit of 1011101111 is "1", which occurs 8 times in 1011101111. Thus a(4) = 8.

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Cf. A004676, A154703, A190480, A191248.

with(StringTools): lim:=100: s:="": for j from 1 to lim do p:=ithprime(j): d:=convert(p,base,2): for k from nops(d) to 1 by -1 do s:=cat(s,d[k]): od: printf("%d, ", nops([SearchAll(s[j],s)])); od: # Nathaniel Johnston, May 27 2011

Module[{p = IntegerDigits[Prime[Range[100]], 2], d}, Array[Count[d = Flatten[p[[;; #]]], d[[#]]] &, Length[p]]] (* Paolo Xausa, Feb 26 2024 *)

Corrected and extended by Nathaniel Johnston, May 27 2011

A164893 Base 10 representation of the string formed by appending primes in base 2.

Original entry on oeis.org

2, 11, 93, 751, 12027, 192445, 6158257, 197064243, 6306055799, 201793785597, 6457401139135, 413273672904677, 26449515065899369, 1692768964217559659, 108337213709923818223, 6933581677435124366325, 443749227355847959444859, 28399950550774269404471037

Offset: 1

Gil Broussard, Aug 29 2009

The subsequence of primes begins: 2, 11, 751. [Jonathan Vos Post, May 26 2010]

			The primes in base 2 (10, 11, 101, 111,...) concatenated by appending give the first four binary terms 10, 1011, 1011101, 1011101111; or 2, 11, 93, 751 base 10.

Charles R Greathouse IV, Table of n, a(n) for n = 1..335 (all terms under 1000 digits)

Cf. A000040, A004676, A007088, A100003, A154703.

nn=20;With[{b2p=IntegerDigits[#,2]&/@Prime[Range[nn]]},Table[ FromDigits[ Flatten[ Take[b2p,n]],2],{n,nn}]] (* Harvey P. Dale, Mar 26 2013 *)

list(n)=my(p=primes(n),s);vector(n,i,s=s<<#binary(p[i])+p[i]) \\ Charles R Greathouse IV, Mar 26 2013

a(n) = A154703(n) [converted from base 2 to base 10]. [Jonathan Vos Post, May 26 2010]

Corrected by Harvey P. Dale, Mar 26 2013

A178388 Concatenation of the first n primes written in base 3.

Original entry on oeis.org

2, 210, 21012, 2101221, 2101221102, 2101221102111, 2101221102111122, 2101221102111122201, 2101221102111122201212, 21012211021111222012121002, 210122110211112220121210021011, 2101221102111122201212100210111101

Offset: 1

Jonathan Vos Post, May 26 2010

			a(4) = Concatenate[prime(1) base 3, prime(2) base 3, prime(3) base 3, prime(3) base 3] = Concatenate[2 base 3, 3 base 3, 5 base 3, 7 base 3] = Concatenate[2, 10, 12, 21] = 2101221.

Rémy Sigrist, Table of n, a(n) for n = 1..174

Cf. A000040, A001363, A004676, A007088, A007089, A019518, A031974, A100003, A154703.

Module[{nn=15,p3},p3=IntegerDigits[Prime[Range[nn]],3];Table[FromDigits[Flatten[ Take[p3,n]]],{n,nn}]] (* Harvey P. Dale, Aug 25 2022 *)

v = 0; for (n=1, 12, d = digits(prime(n), 3); v = v*10^#d + fromdigits(d); print1 (v ", ")) \\ Rémy Sigrist, Aug 07 2017

Edited by N. J. A. Sloane, Jul 02 2017

A189799 Least position k of n (n written in base 2) in the infinite string 101110111110111101100011001110111... (i.e., 23571113171923... in base 2).

Original entry on oeis.org

1, 1, 3, 19, 1, 4, 3, 19, 24, 50, 1, 18, 4, 3, 7, 86, 19, 44, 24, 50, 56, 16, 1, 18, 23, 49, 4, 42, 3, 8, 7, 177, 86, 185, 19, 100, 44, 52, 24, 225, 50, 478, 56, 16, 47, 1, 5, 85, 18, 43, 23, 49, 55, 15, 4

Offset: 1

Juri-Stepan Gerasimov, May 24 2011

			1 appears as (1)0111..., 2 appears as (10)111011..., 3 as 10(11)10111..., 4 as 101110111110111101(100)0...

Cf. A004676, A007088, A154703.

A189799 := proc(n)
        local abin ,nbin ,nlen;
        abin := ListTools[Reverse](convert(A154703(100),base,10)) ;
        nbin := ListTools[Reverse](convert(n,base,2)) ;
        nlen := nops(nbin) ;
        for i from 1 do
                if verify(nbin,[op(i..i+nlen-1,abin)],'sublist') then
                        return i;
                end if;
        end do:
        return 0 ;
end proc:
seq(A189799(n),n=1..55) ; # R. J. Mathar, Jun 07 2011

Corrected by R. J. Mathar, Jun 07 2011

cp's OEIS Frontend

A191233 The number of times that the n-th digit of A154703(n) occurs in A154703(n).

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A164893 Base 10 representation of the string formed by appending primes in base 2.

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A178388 Concatenation of the first n primes written in base 3.

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A189799 Least position k of n (n written in base 2) in the infinite string 101110111110111101100011001110111... (i.e., 23571113171923... in base 2).

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