A051596 -id:A051596 - cp's OEIS frontend

A239751 Numbers whose number of nonzero binary digits is less than their number of nonzero decimal digits.

16, 32, 64, 128, 129, 132, 136, 144, 192, 256, 257, 258, 264, 272, 288, 384, 512, 513, 514, 516, 528, 544, 576, 768, 1024, 1025, 1026, 1028, 1032, 1056, 1088, 1152, 1153, 1154, 1156, 1168, 1184, 1216, 1280, 1281, 1282, 1284, 1288, 1296, 1312, 1344, 1536, 1537, 1538, 1544, 1552, 1568, 1664

Offset: 1

Michael Turniansky, Mar 26 2014

If Hebrew gematria (A051596) were replaced with a "binary gematria" where aleph=1, bet=2, gimel=4, etc., this sequence would be a subset of "numbers whose binary gematria has fewer letters than their original gematria".

Michael Turniansky, Table of n, a(n) for n = 1..200

Cf. A000120, A051596, A055640.

((+⌿(22⍴2)⊤C)<+⌿0≠(5⍴10)⊤C)/C←⍳10000

Select[Range[1664], Less @@ Total /@ Sign /@ IntegerDigits[#, {2, 10}] &] (* Giovanni Resta, Mar 26 2014 *)

n such that A000120(n)<A055640(n).

A339073 Number of strings of Hebrew letters with a gematria value equal to n.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172, 16336, 32656, 65280, 130496, 260864, 521473, 1042434, 2083846, 4165649, 8327214, 16646264, 33276208, 66519792, 132974368, 265818368, 531376129, 1062231296, 2123421181, 4244760561, 8485359561, 16962400080, 33908170232, 67783096912

Offset: 1

Daniel Sterman, Nov 22 2020

A051596-restricted compositions of n.

			The four strings with a gematria of 3 are:
אאא (111)
אב (12)
בא (21)
ג (3)
Note: Hebrew is written right-to-left, which is why the order of the digits appears to be reversed.

Robert Israel, Table of n, a(n) for n = 1..3300
Wikipedia, Gematria

Cf. A051596, A000079.

g:= 1/(1-add(x^i,i=1..9)-add(x^(10*i),i=1..9)-add(x^(100*i),i=1..4)):
S:= series(g,x,101):
seq(coeff(S,x,n),n=1..100); # Robert Israel, Nov 25 2020

Table[SeriesCoefficient[1/(1 - Sum[x^j, {j, Join[Range[9], 10 Range[9], 100 Range[4]]}]), {x, 0, n}], {n, 100}] (* Jan Mangaldan, Nov 27 2020 *)

From Doron Zeilberger, Nov 23 2020: (Start)
G.f.: Sum(a(n)*x^n, n=0..infinity) =
1/(1-add(x^i,i=1..9)-add(x^(10*i),i=1..9)-add(x^(100*i),i=1..4))
= 1/(1-x-...-x^9 - x^10- ... -x^90 - x^100-x^200-x^300-x^400).
Asymptotics:
a(n) ~ 0.50221591060212746248115807725009875743325273964521...*(1.9990196005347377028156443471636402056440270173905...)^n
If alpha is the smallest positive root of P:=1-x-...-x^9 - x^10- ... -x^90 - x^100-x^200-x^300-x^400=0
then the above asymptotic formula is exactly  -(alpha*P'(alpha))* (1/alpha)^n.
(End)

More terms from Robert Israel, Nov 25 2020

A071061 Abjad values of the Arabic letters in the traditional order for abjad calculations.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000

Offset: 1

Koksal Karakus (karakusk(AT)hotmail.com), May 26 2002

The Greek or Ionian numerals are similar, but omit 1000. - Charles R Greathouse IV, Jun 25 2012

F. Lewis, Overview of the abjad numerological system

Subsequence of A037124.

Cf. A051596.

cp's OEIS Frontend

A239751 Numbers whose number of nonzero binary digits is less than their number of nonzero decimal digits.

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A339073 Number of strings of Hebrew letters with a gematria value equal to n.

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A071061 Abjad values of the Arabic letters in the traditional order for abjad calculations.

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