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%I #18 Feb 11 2021 07:33:00
%S 411203,411205,3202114,4111203,4111205,4112023,4112025,5202114,
%T 30211234,30232114,30234114,30252114,30256114,32021114,32032114,
%U 32034114,32052114,32056114,32074114,32076114,32112034,32112074,32302114,32502114,41111203
%N Numbers such that any two adjacent digits sum to a prime and such that any digit 0,...,9 can be inserted somewhere preserving this property.
%C "Inserted" includes the possibility of appending the digit or prefixing it if nonzero.
%C A subsequence of A182175.
%C There are only two terms, a(1)=411203 and a(2)=411205, below 10^6, and six more terms below 10^7, but many 8-digit terms.
%H M. F. Hasler, <a href="/A249405/b249405.txt">Table of n, a(n) for n = 1..124</a>
%e a(n)=411203 is the least member of A182175 such that each of the digits 0-9 can be inserted somewhere such that another term of A182175 is obtained; e.g., 411203[0], 41[1]1203, 41[2]1203, 4112[3]03, 41[4]1203, 4112[5]03, 41[6]1203, [7]411203, 411203[8], [9]411203.
%o (PARI) is(n)={is_A182175(n)||return; n=digits(n); !for(D=0,9,isprime(n[#n]+D)&&next;D&&isprime(n[1]+D)&&next;for(i=3-!D,#n-1,isprime(n[i-1]+D)&&isprime(n[i]+D)&&next(2));return)} \\ A digit D=0 may not be prefixed but may be inserted after the first digit (which is irrelevant for digits > 0).
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Oct 27 2014
%E Data and b-file corrected thanks to a remark by _Hans Havermann_, _M. F. Hasler_, Oct 29 2014
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