# [seqfan] Re: Two neighboring digits sum up to a prime

Jim Nastos nastos at gmail.com
Mon Apr 16 20:13:32 CEST 2012

```Hi Eric, everyone,

The set of numbers with the property that adjacent pairs of digits
sum to a prime is:

2 3 4 5 6 7 8 9 11 12 14 16 20 21 23 25 29 30 32 34 38 41 43 47 49 50
52 56 58 61 65 67 70 74 76 83 85 89 92 94 98 111 112 114 116 120 121
123 125 129 141 143 147 149 161 165 167 200 202 203 205 207 211 212
214 216 230 232 234 238 250 252 256 258 292 294 298 300 302 303 305
307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416
430 432 434 438 470 474 476 492 494 498 500 502 503 505 507 520 521
523 525 529 561 565 567 583 585 589 611 612 614 616 650 652 656 658
670 674 676 700 702 703 705 707 741 743 747 749 761 765 767 830 832
834 838 850 852 856 858 892 894 898 920 921 923 925 929 941 943 947
949 983 985 989
(not in OEIS, even if single-digit numbers are excluded)

Single digit numbers are included here because the set of possible
"adjacent-digit-sums" is an empty set. These are all the candidate
numbers for extended Eric Angelini's proposed sequence.

Starting with initial value of 1, Eric's sequence goes like this:
1 2 3 4 7 6 5 8 9 20 21 11 12 14 16 50 23 25 29 41 43 47 49 83 85 61
65 67 411 111 112 30 32 34 38 52 56 58 92 94 70 74 76 114 98 300 200
202 116 120 203 89 205 207 412 121 123 211 125 212 129 214 141 143 216
147 414 149 230 232 161 165 234 167 416 500 238 302 303 250 252 305
256 502 307 430 258 320 292 321 294 323 298 325 611 432 329 434 341
438 343
(not in OEIS: Eric's original message missed the 14 between 12 and 16.)

If one wants to start this off with 0 instead, then 0,1 is not prime,
so we go with 0,2 and run from there to create:
0 2 1 4 3 8 5 6 7 41 11 12 9 20 21 14 16 50 23 25 29 43 47 49 83 85 61
65 67 411 111 112 30 32 34 38 52 56 58 92 94 70 74 76 114 98 300 200
202 116 120 203 89 205 207 412 121 123 211 125 212 129 214 141 143 216
147 414 149 230 232 161 165 234 167 416 500 238 302 303 250 252 305
256 502 307 430 258 320 292 321 294 323 298 325 611 432 329 434 341
438 343
(not in OEIS.)

I can submit these 3 sequences once my account is created (I haven't
submitted in almost 10 years.. I didn't need an account back then!)
J

On Mon, Apr 16, 2012 at 9:42 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> Hello SeqFans,
> this should be easy to extend:
>
> Smallest integer not yet in S such that two neighboring
> digits of S sum up to a prime:
>
> S = 1,2,3,4,7,6,5,8,9,20,21,11,12,16,50,23,25,29,41,43,47,49,...
> Best,
> É.
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

```