The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A157733 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A157733

a(0)=2, a(1)=3. Then 2 or 22 followed by a string of 3's such that the sum of the digits of a(n) is equal to prime(n).
(history; published version)

#15 by Harvey P. Dale at Tue Jul 06 10:10:40 EDT 2021

STATUS

editing

approved

#14 by Harvey P. Dale at Tue Jul 06 10:10:37 EDT 2021

MATHEMATICA

Module[{nn = 30, t1, t2}, t1 = FromDigits/@Select[Table[PadRight[{2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; t2 = FromDigits/@ Select[ Table[ PadRight[{2, 2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; Union[ Join[ {2, 3}, t1, t2]]] (* Harvey P. Dale, Mar 06 2013 *)

STATUS

approved

editing

#13 by T. D. Noe at Thu Dec 05 12:50:55 EST 2013

STATUS

editing

approved

#12 by T. D. Noe at Thu Dec 05 12:50:50 EST 2013

COMMENTS

The number of twos is 3 - A039701(n) if n > 1. - Curtz

STATUS

proposed

editing

#11 by Wesley Ivan Hurt at Wed Dec 04 11:27:26 EST 2013

STATUS

editing

proposed

#10 by Alonso del Arte at Wed Dec 04 00:08:57 EST 2013

COMMENTS

The number of twos is 3 - A039701(n) if n > 1. - Curtz

If prime(n) is congruent to 1 mod 6, then a(n) starts with 22, but if prime(n) is congruent to 5 mod 6, then a(n) starts with 2. - Alonso del Arte, Dec 04 2013

#9 by Alonso del Arte at Wed Dec 04 00:02:40 EST 2013

COMMENTS

We search for w twos and t threes in prime(n) = 2*w + 3*t. If t = floor(prime(n)/3) would lead to w = 1/2, we decrease t by 1.

The number of twos is 3 - A039701(n) if n > 1.

EXAMPLE

a(3) = 23 because the third prime is 5 and 2 + 3 = 5.

a(4) = 223 because the fourth prime is 7 and 2 + 2 + 3 = 7.

a(5) = 2333 because the fifth prime is 11 and 2 + 3 + 3 + 3 = 11.

#8 by Alonso del Arte at Wed Dec 04 00:00:26 EST 2013

MATHEMATICA

Module[{nn = 30, t1, t2}, t1 = FromDigits/@Select[Table[PadRight[{2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; t2 = FromDigits/@Select[Table[ PadRight[ {2, 2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; Union[Join[{2, 3}, t1, t2]]] (* Harvey P. Dale, Mar 06 2013 *)

STATUS

proposed

editing

#7 by Wesley Ivan Hurt at Tue Dec 03 20:45:43 EST 2013

STATUS

editing

proposed

#6 by Wesley Ivan Hurt at Tue Dec 03 20:44:55 EST 2013

NAME

a(0)=2, a(1)=3. Then 2 or 22 followed by a string of 3's such than that the sum of the digits of a(n) is equal to prime(n).

STATUS

approved

editing