[seqfan] Prime sums of consecutive terms/digits

[Eric Angelini]

Hello SeqFans,
nicely computed by Lars Blomberg, 
here is D where two consecutive terms 
sum to a prime _and_ where two consecutive 
digits  sum also to a prime (commas 
or not). Will 14 show up one day?

D = 1, 2, 3, 4, 7, 6, 5, 8, 9, 20, 21, 16, 111, 112, 121, 120, 29, 212, 11, 12, 125, 234, 149, 230, 203, 216, 143, 258, 305, 252, 167, 432, 161, 116, 123, 214, 165, 202, 129, 238, 303, 298, 321, 250, 207, 412, 307, 612, 325, 232, 141, 256, 505, 292, 147, 416, 503, 294, 323, 434, 389, 438, 349, 474, 347, 414, 329, 492, 385, 676, 525, 656, 507, 430, 211, 498, 341, 470, 383, 476, 521, 650, 23, 830, 741, 658, 523, 838, 343, 850, 583, 856, 567, 494, 707, 614, 705, 616, 565, 652, 529, 832, 921, 1216, 561, 670, 589, 834, 749, 852, 925, 858, 929, 894, 703, 898, 585, 674, 765, 892, 985, 2034, 743, 2058, 941, 1112, 1125, 2038, 3021, 1232, 947, 4112, 989, 2030, 747, 4114, 1123, 2520, 2029, 2020, 2307, 4120, 2023, 2050, 2161, 1212, 949, 2052, 1111, 1230, 767, 4320, 761, 1116, 1121, 1250, 2021, 1238, 923, 2076, 1141, 1252, 1129, 2074, 1143, 2114, 1205, 6116, 1167, 4702, 1147, 4302, 3029, 2070, 2141, 1202, 1149, 2032, 1611, 1120, 2329, 2112, 1207, 4116, 1165, 2056, 1161, 1256, 1203, 2116, 1411, 1432, 3025, 2502, 5021, 1430, 2111, 1416, 5203, 2320, 2121, 1292, 1211, 1476, 7025, 8502, 5207, 6114, 943, 2920, 2167, 6120, 2123, 2120, 2303,…
 
[Lars]:
> The smallest number not used is 14 even up to terms < 10^6.
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Another nice seq would be E where:
- no term is duplicated
- no term is prime
- no sum of two consecutive terms is prime
- no sum of two consecutive digits (commas or not) is prime
- ... E being the lexico-first such seq.

Best,
É.