A064823 -id:A064823 - cp's OEIS frontend

A065253 a(n) = 10*(A064823(n)-1) + A000796(n).

3, 1, 4, 11, 5, 9, 2, 6, 15, 13, 25, 8, 19, 7, 29, 23, 12, 33, 18, 14, 16, 22, 26, 24, 43, 53, 28, 63, 32, 17, 39, 35, 0, 42, 38, 48, 34, 21, 49, 27, 31, 36, 59, 73, 69, 79, 83, 37, 45, 41, 10, 55, 58, 52, 20, 89, 47, 44, 99, 54, 64, 65, 109, 62, 93, 30, 57, 68, 51, 46, 74, 40

Offset: 1

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 26 2001

The sequence would be a permutation of the naturals if each of the digits 0,1,..,9 occur infinitely often in the decimal expansion of Pi. "Inverse": A065254

Cf. A064823, A000796, A065254.

a065253 n = a065253_list !! (n-1)
a065253_list = zipWith (+)
               (map ((* 10) . (subtract 1)) a064823_list) a000796_list
-- Reinhard Zumkeller, Jul 14 2013

terms = 100; Clear[cnt]; cnt[_] = n = 0;
Do[a[++n] = 10 (++cnt[k] - 1) + k, {k, RealDigits[Pi, 10, terms][[1]]}];
a /@ Range[terms] (* Jean-François Alcover, Nov 15 2019 *)

A090626 T(n,k) = if (k-th digit of pi) = (n-th digit of pi) then 1 else 0, 1<=k<=n (pi=3.14159... ), triangular array read by rows.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Reinhard Zumkeller, Dec 12 2003

A064823(n) = Sum(T(n,k): 1<=k<=n).

T(n, k) = 0^((A000796(n) - A000796(k))^2).

cp's OEIS Frontend

A065253 a(n) = 10*(A064823(n)-1) + A000796(n).

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A090626 T(n,k) = if (k-th digit of pi) = (n-th digit of pi) then 1 else 0, 1<=k<=n (pi=3.14159... ), triangular array read by rows.

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