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 A351622 Palindromic primes (palprimes) whose sum of factorials of digits is also a palprime. 1
 2, 11, 101, 1221221, 112111211, 121111121, 144010441, 335414533, 12444144421, 14244144241, 15525152551, 34254145243, 1034450544301, 1044141414401, 1044531354401, 1045341435401, 1053441443501, 1054341434501, 1054431344501, 1055050505501, 1055150515501, 1055500055501, 1104440444011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) has an odd number of digits with the middle digit is 0 or 1 except for the terms 2 and 11. - David A. Corneth, May 05 2022 REFERENCES 1221221 is a term because 1!+2!+2!+1!+2!+2!+1! = 11. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 PROG (PARI) forprime(i=1, 10^12, di=digits(i); if(di==Vecrev(di), s=sum(j=1, #di, di[j]!); ds=digits(s); if(isprime(s) && ds==Vecrev(ds), print1(i, ", ")))) (Python) from math import factorial from sympy import isprime from itertools import count, islice, product myfact = {d:factorial(int(d)) for d in "0123456789"} def ispal(s): return s == s[::-1] def sofod(s): return sum(myfact[d] for d in s) def palprimecandstrs(): yield from ["2", "3", "5", "7", "11"] for digs in count(3, step=2): for last in "1379": for p in product("0123456789", repeat=digs//2-1): left = "".join(p) for mid in "01": # else sofod even (cf. Corneth comment) yield last + left + mid + left[::-1] + last def agen(): # generator of terms for strp in palprimecandstrs(): s = sofod(strp) if ispal(str(s)) and isprime(s): p = int(strp) if isprime(p): yield p print(list(islice(agen(), 23))) # Michael S. Branicky, May 13 2022 CROSSREFS Subsequence of A002385. Cf. A061602. Sequence in context: A069664 A130150 A115941 * A024721 A285199 A339081 Adjacent sequences: A351619 A351620 A351621 * A351623 A351624 A351625 KEYWORD nonn,base AUTHOR Alexandru Petrescu, May 05 2022 EXTENSIONS More terms from David A. Corneth, May 06 2022 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)