A077648 -id:A077648 - cp's OEIS frontend

A153726 Initial digit of Catalan number A000108(n).

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

Offset: 0

Omar E. Pol, Dec 30 2008

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A000030, A008963, A077648, A152669.

First[IntegerDigits[#]]&/@CatalanNumber[Range[0,120]] (* Harvey P. Dale, Jan 20 2014 *)

a(n)=A000030(A000108(n)).

More terms from Harvey P. Dale, Jan 20 2014

A077649 Initial digit of composite numbers.

Original entry on oeis.org

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

Offset: 1

Labos Elemer, Nov 19 2002

Cf. A000030, A002808, A077648.

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[First[IntegerDigits[c[w]]], {w, 1, 128}]
First[IntegerDigits[#]]&/@Complement[Range[150],Prime[Range[ PrimePi[150]]]]  (* Harvey P. Dale, Apr 26 2011 *)

lista(nn) = forcomposite(n=1, nn, print1(digits(n)[1], ", ")); \\ Michel Marcus, Dec 13 2017

a(n) = A000030(A002808(n)).

A093337 Penultimate digits of the primes.

Original entry on oeis.org

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

Offset: 11

Cino Hilliard, Apr 25 2004

Cf. A093336, A077648, A007652.

[Intseq(p)[2]: p in PrimesInInterval(11,600)]; // Bruno Berselli, Feb 14 2013

IntegerDigits[#][[-2]]&/@Prime[Range[5,110]] (* Harvey P. Dale, Apr 08 2019 *)

penult(n) = { forprime(x=11,n, s = Str(x); ln = length(s); pu = mid(s,ln-1,1); print1(pu",") ) } \ Get a substring of length n from string str starting at position s in str. mid(str,s,n) = { v =""; tmp = Vec(str); ln=length(tmp); for(x=s,s+n-1, v=concat(v,tmp[x]); ); return(v) }

A093338 Scan primes, write down initial digit if it is a prime.

Original entry on oeis.org

2, 3, 5, 7, 2, 2, 3, 3, 5, 5, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 2

Cino Hilliard, Apr 25 2004

Cf. A077648.

firstpr(n) = { forprime(x=2,n, fd = eval(mid(Str(x),1,1)); if(isprime(fd),print1(fd",")) ) } \ Get a substring of length n from string str starting at position s in str. mid(str,s,n) = { v =""; tmp = Vec(str); ln=length(tmp); for(x=s,s+n-1, v=concat(v,tmp[x]); ); return(v) }

cp's OEIS Frontend

A153726 Initial digit of Catalan number A000108(n).

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A077649 Initial digit of composite numbers.

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PARI

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A093337 Penultimate digits of the primes.

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Magma

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PARI

A093338 Scan primes, write down initial digit if it is a prime.

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PARI